Question

How do you evaluate `\log _ { \frac { 3} { 4} } \frac { 27} { 64}`?

Answer 1

`log_(3/4)(27/64)=3`

Explanation:

Let `log_(3/4)(27/64)=x`,

then according to definition of logarithm

`(3/4)^x=27/64=3^3/4^3=(3/4)^3`

Hence `x=3` i.e. `log_(3/4)(27/64)=3`.