Question

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

log16 64

Answer 1

`(3)/(2)`

Explanation:

Changing Bases to Evaluate Logarithms

`log_(16)(64)`

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_(16)(64)`

`log_(16)(a)= (log 64)/(log 16)`

64 is 4^3 and 16 is 4^2

`log_(16)(a)= (log 4^3)/(log 4^2)`

Move the exponent before log

`(3log 4)/(2log 4)`

top and bottom has same log so cancel it out

`(3)/(2)`