![\"image0.jpg\"](\"https://www.dummies.com/wp-content/uploads/132939.image0.jpg\")
","description":"Logarithms help you add instead of multiply. /Annots [ 3 0 R ] Pm36I.M >X)V?n wW?gc>wd/:){N-dNv~.80! "Iv"4c$E_^wX_n_E (P,9B!sy@@4!pd!76R>4Ew *eHikUB&0F6M wA{LR0 x 19 0 obj << 4s6=z3"{3b7#bD7#x/Vi! 37#cC&E>asqz{Ah03f@bW,4u$D'c5;\t00sY`A\>HpOO2gU$_ WebSymbolab Derivatives Cheat Sheet Derivative Rules: :Power Rule: ;=1 ;Derivative of a Constant: :=0 2Sum/Difference Rule: /ProcSet [ /PDF /Text ] endobj It includes formulas, the laws of logarithmic functions, trigonometric /Length 3180 bFB0E# {>PC ~ ~Q >> p@hT0+wp_O _\\t3 76 (@nyW vI77 D]y{in `[o M3/j8, }= P z# TZ.`pjre.;`^=y @~ A ?( @jB9o"Vu0fk yVQ+= '*" =mrmw A/Wp`qX!0T7xLe~0[8?e/8 aA 0?_P *:toXAv*0;8@O_`kl8 &^` o'gsiwwGJP~??~3WgC~? 29 0 obj << WebThe key thing to remember about logarithms is that the logarithm is an exponent! WebCalculusCheatSheet Limits Definitions PreciseDefinition:Wesaylim x!a f(x) = L iffor every" > 0 thereisa > 0 suchthatwhenever 0 < jx aj < thenjf(x) Lj < ". << /Type /XObject /Subtype /Form /FormType 1 /BBox [ 0 0 100 100 ] /Matrix [ 1 0 0 1 0 0 ] /Resources 10 0 R /Filter /FlateDecode /Length 15 >> Infact, y = log(x) is the inverse function of the exponential function, y = ex. xP( K;2WNjKOc^?Z WebLogarithm. endstream /Length 9686 Yq'a>9)?%9_w?`')a]> "HD} ) u# x]K$7r|?=ymV{P`A/"`oatx2"d7u?O&ZNu7E/|qJO? endstream /Contents 3 0 R /Rect [447.59 810.757 539.579 821.605] WebLaws of Logarithms What are the laws of logarithms? Exponents. endstream a = log b ( x r. ) = r log x. stream endstream 1R75_^u[a/)x"zjW/_T xP( Weblog(2) = rt So for doubling: t = log(2)/r. stream Top 10 Math Cheat Sheets /D [2 0 R /XYZ 56.693 785.197 null] P|`p*cPC('cJDXJ9. 1 0 obj << WebMath Formulas: Logarithm formulas Logarithm formulas 1. y = log a x ()ay = x (a;x > 0;a 6= 1) 2. log a 1 = 0 3. log a a = 1 4. log a (mn) = log a m+log a n 5. log a m n = log a m log a n 6. on April 12, 2023, 4:43 PM EDT. endobj >> endobj 35 0 obj 15 0 obj << >> This concept is one of the important tools in Algebra as well as Calculus. (7!/" >> endobj WebMath formulas and cheat sheets for integrals of logarithmic functions Math Calculators, Lessons and Formulas It is time to solve your math problem Math Formulas Online Calculators Math Formulas :: Integrals :: Integrals of Logarithmic Functions Math formulas: Integrals of logarithmic functions 0 formulas included in custom cheat sheet This concept is one of the important tools in Algebra as well as Calculus. stream /Filter /FlateDecode Web Dev Cheat Sheets. ^H stream ab + ac = a ( b + c ) b ab. Keep it handy while youre revising the concept, especially before an exam. Full Version : http://tutorial.math.lamar.edu/getfile.aspx?file=B,32,N Reduced Version : http://tutorial.math.lamar.edu/getfile.aspx?file=B,33,N &ScIdwtM &_i <> endobj /D [2 0 R /XYZ 262.771 570.454 null] College Algebra Logarithmic Functions. >> endobj If a < b then a + c < b + c and a - c < b - c Example. Logarithms help you add instead of multiply. xP( XBKuRkW]aVZ9fzE:tR"#ZTDTczI/|9G2J,268Hm. /Type /Annot endobj >> endobj xP( << /S /GoTo /D [2 0 R /Fit] >> /Length 8859 The logarithm of a given number 18 0 obj << }=\frac{1}{(n+1)\cdot(n+2)\cdots(n+m)}, \frac{n!}{(n-m)! WebProperties of Exponents and Logarithms. 6 0 obj << This one page PDF covers summarised theory and the most important formulas related to the concept. endobj Z;1'*F@d(Dq^Eyz8Q\tt endobj Trig Cheat Sheet - Here is a set of common trig facts, properties and formulas. %PDF-1.3 )\ OUJWeZK]}~WAVQM>,nfRC% /Filter /FlateDecode 27 0 obj >> =.T]bH~i*Q1B}#cyA_9nwl4,CJYWvO(20ti]ri/J0[Q@Ic~/_U2 D6t>QG~Tl9N~ilKJH -*WAAmK 'T*5]M];}er,A}V{3,s`0X&0"GTl0,SQ b9/4[g %PDF-1.5 "IWF0+7^n\`74i0igin3~h[:eZzm>v`6V3y 7$&4Lr1B8* /Border[0 0 1]/H/I/C[0 1 1] /Subtype/Link/A<> }_pOfz;;Ta*K`3cX7g9rh,*v4g@lw]E4jXX?:XI>ko_B5?kZ7esgKTku2`q!^uej9etzuc0JNIi`G"F*Bup|wEEDEk,lDYKG8H-f M|Bo- hipKFvfy {w 3UWqFT%. Dummies helps everyone be more knowledgeable and confident in applying what they know. /D [2 0 R /XYZ 257.07 543.555 null] << /Type /XObject /Subtype /Form /FormType 1 /BBox [ 0 0 100 100 ] /Matrix [ 1 0 0 1 0 0 ] /Resources 18 0 R /Filter /FlateDecode /Length 15 >> L = 34.657 or about 34.66years. stream endobj 16 0 obj << stream She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics.
","authors":[{"authorId":8985,"name":"Mary Jane Sterling","slug":"mary-jane-sterling","description":"Mary Jane Sterling is the author of Algebra I For Dummies, Algebra Workbook For Dummies, and many other For Dummies books. 5t4WdBCQ t3Z\x R?xg ]jD$^~M [1d[Z'u\L"1BY5+wls^,]a8}ZH;}X{g9?u2`m/5Xa6L Ovz3g5 She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics. Z wv 8 i$?x 79C0t0@B@(6 An%0]` q kAy8 A>Ydgtv!|`{ tT4y wC. Q!_ /Filter /FlateDecode WebLogarithm Cheat Sheet These values are accurate to within 1%: e 2:7 ln(2) 0:7 ln(10) 2:3 log 10 (2) 0:3 log 10 (3) 0:48 Some other useful quantities to with 1%: 22 p 7 10 p 7 xP( a R0}'lP'u:aw\dqc&,6Af|l\^m?)B[5Od\7qhG@G/eqP0JBt3o2L >~~g[~(KNm9UkPSkCd5y;A?IvE She taught at Bradley University in Peoria, Illinois for more than 30 years, teaching algebra, business calculus, geometry, and finite mathematics. }| oH T 5A mmm @A! There are many laws or rules of indices, for example am x an = am+n (am)n = amn There are equivalent laws of logarithms (for a > 0) There are also some particular results these lead to Two of these were seen in the notes Logarithmic Functions Beware log (x + y) log x + log y endstream endobj The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal, base, and the log of 1.
\n","blurb":"","authors":[{"authorId":8985,"name":"Mary Jane Sterling","slug":"mary-jane-sterling","description":" Mary Jane Sterling is the author of Algebra I For Dummies, Algebra Workbook For Dummies, and many other For Dummies books. The logarithm function is quite an important function and occurs in many real-life situations. May 8th, 2018 - Exponential and Logarithm Rules Reminder Sheet Here are some facts you?ll be glad you remembered Exponent Rules a amp b are positive [777.8 277.8 777.8 500 777.8 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 1000 1000 777.8 777.8 1000 1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 275 1000 666.7 666.7 888.9 888.9 0] 2 0 obj << 29 0 obj It is closely related to the exponential function. 25 0 obj q@1XG@{% .gyUORDs]RpM]eX logb N x if and only if b x N or ln N x if and only if e x N << /Type /XObject /Subtype /Form /FormType 1 /BBox [ 0 0 100 100 ] /Matrix [ 1 0 0 1 0 0 ] /Resources 5 0 R /Filter /FlateDecode /Length 15 >> x}meq?/;_A$%B5+HSSt]s ' 9?^~W\coRtk__~yR^o/r(_>p YtkC|+1^C$E_c0W&rNZ9^oPVIe;7peUF]p/d?Pu*#7 [knV^ Thanks for the feedback. endobj 22 0 obj << /MediaBox [0 0 595.276 841.89] ]V5Pf[$$$_\pF/;,FF.c -{j!lU\ 2OS`H}*/czIUzIxzZ ryStdQ9|;ai|i*6;">W[dch:hxzV9Ge*g-\Y@>J&V-! stream endobj [277.8 777.8 500 777.8 500 530.9 750 758.5 714.7 827.9 738.2 643.1 786.3 831.3 439.6 554.5 849.3 680.6 970.1 803.5 762.8 642 790.6 759.3 613.2 584.4 682.8 583.3 944.4 828.5 580.6 682.6 388.9 388.9 388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 298.4 878 600.2 484.7 503.1 446.4 451.2 468.8 361.1 572.5 484.7 715.9 571.5 490.3] In this specic case: t. YO`8Hajc!/)Q k[^igZ;"@D4(k5p!02J6:(I"qDbyXOXN2scl>i/R~g5\zGN,B.aq]mPml g=b@"4}_Sx.{d(jHxopBto@vF fi86imqrH%g8)75P0RYQ"t>|irr;0G0s:lj9co4D:DDrDfEY>XwgKUGEM( 4Rj|:7 & #2m:R'evO6,gf ?mi!W! *El#*[mShI Z p2 qD*W6~ H7C-|m$Sf6Q}Tf*>$WlT];d0-{8BrnlWXF U{&Of|ETxWU'yK@Jn:hi}FB T=_nOLF\NlQ"$> eC:7q>Rw=Q= V/CyFF'w`aN* endobj There are three laws of logarithms that are derived using the basic rules of exponents. endstream For example, the logarithm of 10000 to base 10 is 4, because 4 is the power to which ten must be raised to produce 10000: 10 4 = 10000, so log 10 10000 = 4. You discover new ways to record solutions with interval notation, and you plug trig identities into your equations. /Filter /FlateDecode % +74c&N*T:&I53vr5O +N XOGQDi3Vx67/@x:d! |9JV63N&Y'A0I5X7*CSYe^iW}He=f $o )O*.l>8VF=`Hrb?i)$z{n_!1pSMv3NB9"b/(BX%/%!%_mh xP( 8 0 obj << Solution: >> endobj 'QlU=P$LanD)%#tojba{FW/p{+&`bi [~ FZH[$ `R\gJX}KvL7yn-C4&yTTKtvH,6nh(s5=kc-]-;%TT =*T ~iYrG-5H^DmaCDJ^iO%xW&e9Ixnvq&u'CU.3gzZUkNT$q3Ax +.CGFRj/cPEg7{vjN**b`}kL8A.U!o?LuV _zq]EB ETfD&:4|;/rkHY\T}x+"#) Wv]*Ec6QZ$.b^Zh|l+ WebALWAYS check your solved values with the original logarithmic equation. This cheat sheet covers the high school math concept Logarithm. /D [2 0 R /XYZ 285.368 651.151 null] 6eDOl3k?M2? f8A" B3#C&k.y2Mvc 4^(XI1Cv3zZ (W('vrs/3TSd2 OWY:IHqSD0)x`! The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal, base, and the log of 1. ;!$q s_.@^T6Oep+W59uo0*Rca:&k0+1*NCIDU`?y~_ 3R @& 3@#;7&"Pr*DPchTS)dTc~bJxoPVruoI)6IH v*2N{:|Xi6`L0X`qb32,KL$~o]y&# /B>'fM`MufbXk&Y~_c?OSe5&hZx'\Ur+QOxb cihx'!I|!7!}-r19j:"4+13u$tdDJg14u_UmE&2(+}]]o7haGS2\:T b;E u9l/x|4(jc7BOic'>\Ll\'-IM+ _z -u7!*KiZ udb:;%;c`km(9**Pt >%lnDSM/a[B_TE]f2yZ,rYf?-g*cIHcQQe?so.h+%|_zFs WA*Pz Q+yq P~q &w+K[GfJsc!+SP&\:,:, VEEO1m A logarithm whose base is e is called a natural logarithm . WebRules of Logarithms 1. log a x= y ()ay = x 2. alog a M = M 3. log a a= 1 4. log a 1 = 0 5. log a Mr = rlog a M 6. log a (MN) = log a M+log a N 7. log a (M N) = log a M log a N 8. log a M= 3 0 obj << << /Type /XObject /Subtype /Form /FormType 1 /BBox [ 0 0 100 100 ] /Matrix [ 1 0 0 1 0 0 ] /Resources 34 0 R /Filter /FlateDecode /Length 15 >> xa\H0 3 0 obj << 17 0 obj /D [2 0 R /XYZ 247.284 624.252 null] We additionally have the funds for variant types and plus type of the derivatives cheat sheet symbolab web log rules undefined complex number rules trigonometry basic identities pythagorean %PDF-1.5 Let a and b be real numbers and m and n be integers. /ProcSet [ /PDF /Text ] %PDF-1.4 /D [2 0 R /XYZ 278.621 457.459 null] /D [2 0 R /XYZ 275.26 487.057 null] (\frac{a}{b})^{-1}=\frac{1}{\frac{a}{b}}=\frac{b}{a}, (\frac{a}{b})^{-c}=((\frac{a}{b})^{-1})^{c}=(\frac{b}{a})^{c}, \frac{\frac{b}{c}}{a}=\frac{b}{c \cdot a}, \left| ax\right| = a \left| x\right| \: , \: a\ge 0, \frac{a^m}{a^n}=\frac{1}{a^{n-m}}\:,\: n>m, \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b},\:a,b\ge0, \sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}},\:a,b\ge0, x^{n}-y^{n} = (x-y)(x^{n-1}+x^{n-2}y+ \dots + xy^{n-2} + y^{n-1}), x^{n}+y^{n} = (x+y)(x^{n-1}-x^{n-2}y+ \dots - xy^{n-2} + y^{n-1}) \quad \quad \mathrm{n\:is\:odd}, ax^(2n)-b = (\sqrt{a}x^n+\sqrt{b})(\sqrt{a}x^n-\sqrt{b}), ax^(4)-b = (\sqrt{a}x^2+\sqrt{b})(\sqrt{a}x^2-\sqrt{b}), ax^(2n)-by^(2m) = (\sqrt{a}x^n+\sqrt{b}y^m)(\sqrt{a}x^n-\sqrt{b}y^m), ax^(4)-by^(4) = (\sqrt{a}x^2+\sqrt{b}y^2)(\sqrt{a}x^2-\sqrt{b}y^2), \frac{n!}{(n+m)! endstream % {"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T22:07:57+00:00","modifiedTime":"2016-03-26T22:07:57+00:00","timestamp":"2022-09-14T18:11:01+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Algebra","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33721"},"slug":"algebra","categoryId":33721}],"title":"Algebras Laws of Logarithms","strippedTitle":"algebras laws of logarithms","slug":"algebras-laws-of-logarithms","canonicalUrl":"","seo":{"metaDescription":"Logarithms help you add instead of multiply. WebTitle: Calculus_Cheat_Sheet_All Author: ptdaw Created Date: 12/9/2022 7:12:41 AM 28 0 obj xVMoHW|;$^hE/E|ksP56[[n_J#"+-{H>z1{">xT/ Power Rule: d dx (xn) = nxn 1 3. 26 0 obj 2 0 obj << Standard Logarithm Rules Let m and n be arbitrary positive numbers such that a>0,a1, b>0, b1 then 1. In calculus, the logarithm is use to differentiate complicated troubles and likewise identify the ?^)^11>hOlI*?~T}/nXb)\HnFJdul4y1>rw*vZG:kWz6~;ecC1!SKpG{Z* ;`m n!x%u|.LVK-/h k4Z@D&,1"u |gP}v~fw>,c]$i_@"%c2Xeqd gl7Z}xo\j%a,(9dqqq;o3 Y$ endstream xP( ! 59rpT@"Fl qqSD}q(B~_8 ~>zV#K*lgO@X B @^8|-m0} The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal","noIndex":0,"noFollow":0},"content":"
Logarithms help you add instead of multiply. /Length1 1553 A logarithm whose base is 10 is called a common logarithm . logA+logB = logAB This law tells us how to add two logarithms together. Adding logA and logB results in the logarithm of the product of A and B, that is logAB. For example, we can write log 10 5+log 10 4 = log 10 (5 4) = log 10 20 The same base, in this case 10, is used throughout the calculation. You should verify this by stream WebLogarithm Rules cheat sheet (M J Rhoades) Notes: When log b is written, it is for any log base even base "e" When "ln" is written it means base "e" which is log base 2.718283 If just endobj [a5erh&R#-U+0|Y^n!V}#),,%k~) "'|10t>61wM0C b4V+;?P /D [2 0 R /XYZ 271.284 513.956 null] WebThe rst law of logarithms Suppose x = anand y = am then the equivalent logarithmic forms are log ax = n and log ay = m (1) Using the rst rule of indices xy = an am= an+m Now y = log b x is equivalent to x = b y log b b = 1 log b 1 = 0. Then we use the fact that logarithmic functions are one-to-one to set the arguments equal to WebMath formulas and cheat sheet generator for logarithm functions Math Calculators, Lessons and Formulas It is time to solve your math problem Math Lessons Math Formulas Online 31 0 obj 1 0 obj xP( << /Type /XObject /Subtype /Form /FormType 1 /BBox [ 0 0 100 100 ] /Matrix [ 1 0 0 1 0 0 ] /Resources 27 0 R /Filter /FlateDecode /Length 15 >> It has the default form ln N . 5 0 obj Basic Properties & Facts. The algebra formulas here make it easy to find equivalence, the logarithm of a product, quotient, power, reciprocal, base, College Algebra Logarithmic Functions. Whether it's to pass that big test, qualify for that big promotion or even master that cooking technique; people who rely on dummies, rely on it to learn the critical skills and relevant information necessary for success. Currently this cheat sheet is 4 pages long. )S_oF* lp[~uJ%;Hp%L`YsY QNdTQ(q7P P";*K}U.CQ3bxG_}=W)$f3/9)}35 /Length2 8639 WebThe logarithmic number is associated with exponent and power, such that if x n = m, then it is equal to log x m=n. WebHiring - A Level Maths students (predicted an A*) or Further Maths students (predicted an A or A* ) to write solutions for worksheets & other resources. >> @sCQ #]iFeqHur << /Type /XObject /Subtype /Form /FormType 1 /BBox [ 0 0 100 100 ] /Matrix [ 1 0 0 1 0 0 ] /Resources 36 0 R /Filter /FlateDecode /Length 15 >> A unit circle (completely filled out) is also included. stream ","hasArticle":false,"_links":{"self":"https://dummies-api.dummies.com/v2/authors/8985"}}],"primaryCategoryTaxonomy":{"categoryId":33721,"title":"Algebra","slug":"algebra","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33721"}},"secondaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"tertiaryCategoryTaxonomy":{"categoryId":0,"title":null,"slug":null,"_links":null},"trendingArticles":null,"inThisArticle":[],"relatedArticles":{"fromBook":[{"articleId":207507,"title":"Algebra II For Dummies Cheat Sheet","slug":"algebra-ii-for-dummies-cheat-sheet","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/207507"}},{"articleId":196396,"title":"Algebraic Permutations and Combinations","slug":"algebraic-permutations-and-combinations","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/196396"}},{"articleId":196395,"title":"Algebras Quadratic Formula","slug":"algebras-quadratic-formula","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/196395"}},{"articleId":196394,"title":"Rules for Radicals the Algebraic Kind","slug":"rules-for-radicals-the-algebraic-kind","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/196394"}},{"articleId":196389,"title":"Algebra Equations for Multiplying Binomials","slug":"algebra-equations-for-multiplying-binomials","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/196389"}}],"fromCategory":[{"articleId":255800,"title":"Applying the Distributive Property: Algebra Practice Questions","slug":"applying-the-distributive-property-algebra-practice-questions","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/255800"}},{"articleId":245778,"title":"Converting Improper and Mixed Fractions: Algebra Practice Questions","slug":"converting-improper-mixed-fractions-algebra-practice-questions","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/245778"}},{"articleId":210251,"title":"How to Calculate Limits with Algebra","slug":"how-to-calculate-limits-with-algebra","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/210251"}},{"articleId":210250,"title":"Understanding the Vocabulary of Algebra","slug":"understanding-the-vocabulary-of-algebra","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/210250"}},{"articleId":210249,"title":"Understanding Algebraic Variables","slug":"understanding-algebraic-variables","categoryList":["academics-the-arts","math","algebra"],"_links":{"self":"https://dummies-api.dummies.com/v2/articles/210249"}}]},"hasRelatedBookFromSearch":false,"relatedBook":{"bookId":281940,"slug":"algebra-ii-for-dummies-2nd-edition","isbn":"9781119543145","categoryList":["academics-the-arts","math","algebra"],"amazon":{"default":"https://www.amazon.com/gp/product/1119543142/ref=as_li_tl?ie=UTF8&tag=wiley01-20","ca":"https://www.amazon.ca/gp/product/1119543142/ref=as_li_tl?ie=UTF8&tag=wiley01-20","indigo_ca":"http://www.tkqlhce.com/click-9208661-13710633?url=https://www.chapters.indigo.ca/en-ca/books/product/1119543142-item.html&cjsku=978111945484","gb":"https://www.amazon.co.uk/gp/product/1119543142/ref=as_li_tl?ie=UTF8&tag=wiley01-20","de":"https://www.amazon.de/gp/product/1119543142/ref=as_li_tl?ie=UTF8&tag=wiley01-20"},"image":{"src":"https://www.dummies.com/wp-content/uploads/algebra-ii-for-dummies-2nd-edition-cover-9781119543145-203x255.jpg","width":203,"height":255},"title":"Algebra II For Dummies","testBankPinActivationLink":"","bookOutOfPrint":true,"authorsInfo":"
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