Question

Evaluate each logarithm. Round your answer to the nearest ten thousandth.

Answer 1

Answer:

1. 1.685

2. 16.828

Step-by-step explanation:

1. log_5 15

To evaluate this logarithm you use the following formula:

$Log_ab=\frac{log_{10}b}{log_{10} a}$

by replacing you obtain:

$log_5 15=\frac{log_{10} 15}{log_{10}5}=\frac{1.176}{0.698}=1.685$

hence, the answer is 1.685

2. -3ln(1/e4/5)

to solve this logarithm you use the following properties:

$ln(a^m)=m\ ln(a)\\\\ln(\frac{a}{b})=ln(a)-ln(b)\\\\ln(e^m)=m$

$ln(1)=0$

By applying all these properties you obtain:

$-3ln(\frac{1}{\frac{e^4}{5}})=-3[ln(\frac{1}{e^4})-ln(5)]=-3[ln(1)-ln(e^4)-ln(5)]\\\\-3ln(\frac{1}{\frac{e^4}{5}})=-3[0-4-1.609]=16.828$

hence, the answer is 16.282