Question

Changing Bases to Evaluate Logarithms In Exercise, use the change-of-base formula and a calculator to evaluate the logarithm.

log4 125

Answer 1

`log_(4)(125)=3.48289`

Explanation:

Changing Bases to Evaluate Logarithms

`log_(4)(125)`

Apply change of base formula'

`log_b(a)= (log a)/(log b)`

log term should be the numerator and denominator is the log base

`log_(4)(125)`

`log_(4)(125)= (log 125)/(log 4)`

125 can be written as 5^3

`log_(4)(125)= (log 5^3)/(log 4)`

move the exponent before log

`log_(4)(125)= (3log 5)/(log 4)`

Now use calculator to evaluate the log

`log_(4)(125)=3.48289`