1) Write the following in exponential form log_(9)27=(3)/(2) 2) Write each of the following in logarithmic form 16^1/4=2 Evaluate each of the following logarithms without the use of a calculator. 3) log_(4)(1)/(2)= 4) log_(8)4= 5) log_(3)81= 6) log_(4)0= Write each of the following as the sum or difference of logarithms. 7) logsqrt [4]((x+1)^3(x-2)^2) 8) log_(5)(6x^2)/(11y^5)z 9) log_(2)(sqrt [5](3(x+2)^3))/(x-1) 10) log_(3)(sqrt (5x^5y^3))/(sqrt [3](z^2)) Rewrite each of the following logarithmic expressions using a single logarithm. 11) (1)/(3)log6+(1)/(3)logx+(2)/(3)logy 12) ln(x+3)-ln(2x+5)+2ln(x-1) 13) 3log_(4)x-5log_(4)y+2log_(4)z 14) log_(3)(x+2)+log_(3)(x-2)-log_(3)(x+4) Using a calculator, evaluate each of the following.Round all answers to three decimal places. 15) log_(3)12 16) log_(6)17 17) log_(3)(1)/(5) 18) log_(4)8 Solve each of the following logarithmic equations. (Round any solutions with decimals to three decimal places) Always check for extraneou.roots! 19) log_(3)(x+5)+log_(3)(x+3)=log_(3)35 20) 2log_(3)x-log_(3)(x-2)=2

Question

Pergunta

Answer 1

1)

$9^{\frac{3}{2}}=27$
2)

$\log_{16}2=\frac{1}{4}$
3)

$\log_{4}\frac{1}{2}=-\frac{1}{2}$
4)

$\log_{8}4=\frac{2}{3}$
5)

$\log_{3}81=4$
6)

$\log_{4}0$ is undefined
7)

\log\sqrt[4]{(x+1)^{3}(x-2)^{2}}=\frac{1}{4}\log(x+13}+\frac{1}{4}\log(x-2)^{2}

$\log\sqrt[4]{(x+1)^{3}(x-2)^{2}}=\frac{1}{4}\log(x+13}+\frac{1}{4}\log(x-2)^{2}$
8)

$\log_{5}\frac{6x^{2}}{11y^{5}z}=\log_{5}6x^{2}-\log_{5}11y^{5}z$
9)

$log_{2}\frac{\sqrt[5]{3(x+2)^{3}}}{x-1}=\log_{2}\sqrt[5]{3(x+2)^{3}}-\log_{2}(x-1)$
10)

$log_{3}\frac{\sqrt{5x^{5}y^{3}}}{\sqrt[3]{z^{2}}}=log_{3}\sqrt{5x^{5}y^{3}}-log_{3}\sqrt[3]{z^{2}}$
11)

$\log_{6}3x^{\frac{1}{3}}y^{\frac{2}{3}}$
12)

$\ln\frac{(x+3)(x-1)^2}{2x+5}$
13)

$\log_{4}\frac{x^3z^2}{y^5}$
14)

$\log_{3}\frac{(x+2)(x-2)}{x+4}$
15)

$\log_{3}12\approx2.261$
16)

$\log_{6}17\approx1.732$
17)

$\log_{3}\frac{1}{5}\approx-1.465$
18)

$\log_{4}8\approx1.292$
19)

$x\approx2.449$
20)

$x\approx3.000$