Question

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

1. Log5 15

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

Answer 1

1. 1.685

2. 16.828

Explanation:

1. log_5 15

To evaluate this logarithm you use the following formula:

`Log_ab=(log_(10)b)/(log_(10) a)`

by replacing you obtain:

`log_5 15=(log_(10) 15)/(log_(10)5)=(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((a)/(b))=ln(a)-ln(b)\\\\ln(e^m)=m`

`ln(1)=0`

By applying all these properties you obtain:

`-3ln((1)/((e^4)/(5)))=-3[ln((1)/(e^4))-ln(5)]=-3[ln(1)-ln(e^4)-ln(5)]\\\\-3ln((1)/((e^4)/(5)))=-3[0-4-1.609]=16.828`

hence, the answer is 16.282