University:
Bradley University
Course:
MTH 114 | Precalculus
Academic year:

2022
Views:

272

Pages:

8
Author:

Gudrunecg9m

- 3-4 5 Pre-Calculus Test 33 & 3.4 Name Miss STUDY GUIDE Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 1) 1) log 7 (7x) 2) log 5 (125x ) 1 14) j(log4 x + log4 y ) 2) 15) log x + log ( x2 - 169 ) 7 log (x - 13) rrO j 3) " rie ~ 4) 3) log 3 4) lo§ 4 ^ 5 f »2^ - 3 6) logn xlO . 19 17) log 0.4 n x+2 8) log 5 x4 18) 4 X = 64 8) 19) 4(3X 7) = I 6 19) 20) 9X + 1 = 27* " 10 20) - \ Solve the exponential equation. Express the solution set in terms of natural logarithms, 10 ) 21) 4 x + 8 = 3 21) 22) e2* = 7 22) ° H ) 2 1ogx 3 + 12) 7 In x 18) 9) 9) log ° 5 125 Z 17) 7) _- r 15) QUESTIONS 18-33 You must show work. NO WORK! NO CREDIT! Solve the equation by expressing each side as a power of the same base and then equating exponents. 6) Ify - log Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 16) 16) log 28 3 5) ~ 7) log 2 14) logx 3 11) - - j In y 12) - - 13) 13) 31n (x 8) 10 In x Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 23) 23) 7X = 6X + 7 Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. 24) 24) log 3 x = 5 25) 2 + 4 In x = 9 1 25) 26) log x + log (x - 15) = 2 4 4 26) 27) log (x + 3) = 1 + log (x 3 3 - 1) 27) 4) = log (4x - 2 ) 28) 29) log x2 = log (4x + 5) 6 6 29 ) 30) log x + log (x -1) = log 72 30 ) 28) log (x 31) 21og x + - log 5 = log 180 Solve the problem. 32) Find out how long it takes a $2600 investment to earn $500 interest if it is invested at 7% compounded semiannually. Round to the nearest tenth of a year. Use the formula J A = P 1+ 31) 32 ) — r V. n 33) The formula A = 132 e0 -033t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 210 thousand ? 33) 2 Answer Key Testname: 3.3&3.4TESTBLOCKSG 1) 1 + log 7 x 2) 3 + log . x 3) log 7 - log 5 3 3 4) 2 - log x 4 5) 2 - In 3 6) 101ogn x j > 7 log 2 y 7 - 8) log (x + 2 ) 4 log x 5 5 9) l o g x | 5 " 3 10) logbx + 51ogby - 81ogbz 11) logx 27 x7 ,2) ta — 4y 13) In - 8)3 (X xlO -/ 3/ 14) log4 s xy is) log 16) 3.0331 17) -3.2134 18) {3} 19)|3) 20) 32 In 3 21 ) - 81 t In 4 22) } 23) 81.36 24) ( 243 ) i{ - l lZlFb r -6.9l 3o «} 25 e 7 ^ 26) (16) 27){3} 28){2} 29 ) (5, -1) 30) (9 ) 31) (30 ) 32) 2.6 years 33) 2012 S.354 U 3 \ % oO <5 M O' i " IL.O JZ O ^ Is (J \\ X ’ Ms cP > !i >< 0 J e ** „.) «> fs O’ • X J — H> C 1 « mm —^ Q> - ^ ^ \J i ; ^ r . N i I ( 5 I I i I i 1s t i! o 5 K X. 4 4 ,*® h* i o l tl 0 i i S • • ! : : ; ! \ » i \ rs\ M • i ! s I l I ; i i : * i ' 2 I \ I i I I . § f I < ! 1 u . / 1 Sj ii 11 ^ ?£J- ^ 1 f V «1 i -J -J V X N Ho II.'A Q s $ 1 * x: x" \ o ^ vl ' o »»» \ X j : x; ' I • It < t t £ 1 of / : j X r\ U2 I i : ? > << •: I ! ? i I 5 i i § t s \ ! 5 I .a O \ ^-M »> T ^. _ J \ 0» 1 5 i f x: jr L>r X £ *p i oo , 4 Nx

< \ \ I V ,* > ^ ** » __ T / 1 • > o * -GL I X o oJ stsswwiiS * J 0 4s»»^• ' *- N ii /0 i . * ^ -» « (R t3S ! N >< L-O JD x -4 rx rN CJ JC >< 4- rX> rX\ ^ 3 ! ;] S5-«£ -C j E C-Q i o O jr X X . S* mo r i ' O yr f >03 p ' Wff4 r i. \ toV - 1-VM ? x X x !nX -- II loerL 2 4 2 * - UP *r r 11 f dx £ taka-ti) - ic — ' x t 7A tx ~ 1 2 =,y 3 - 7 3 £ X - lV Xt 3 3yX - 3 ^ / )/f i:t3-3 x- i r * 1 H \~ LXI \oa > j ^ £ * to ' Z Z N 4. X. -+ a t 6 3 ' , 2 v =2 ' * - . " 1 W I 1 ** MT .jl vr* **» , ** * -- ' "•• V* v .- J ya“ Hx + 5 X ^ - MX:5 -- 0 ( . - Fo) 2 i kj X>d - f / s, X -- i*' 2 = !0Q u (li X to ) X vi> 1 * KJ *N ' ( 2 \ t • •* *<** ^ 0 X ~- 5.75 KM = X S ' ^ til X ~I I - J ’ 1 6 3 = XCX \ {« = X ''2 15 V - ~ ' I t- n x II *MV M :/ f\ n 1 r \ \ 26) 27) log 3 (x + 3) = 1 + log 3 (x - 1) 27) 28) log (x + 4) = log (4x - 2 ) 28) 29) log x2 = log (4x + 5) 29 ) 30) log x + log (x -1) = log 72 30) 4 4 / - .6) log x + log (x 15) = 2 ^ ^ - 31) 21og x log 5 = log 180 Solve the problem. 32) Find out how long it takes a $2600 investment to earn $500 interest if it is invested at 7% 31) 32) compounded semiannually. Round to the nearest tenth of a year. Use the formula J A = P 1+ — r n >t. 33) 33) The formula A = 132 e0.033t models the population of a particular city, in thousands, t years after 1998. When will the population of the city oP sO • reach 210 thousand? as 1 n = V221 2 \0 = Ri2 c . O OS'i-fc Vjt -20^ 2

Solve 2 ln 3 = ln(x - 4) x = 9 x = 10 x = 13

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