Question

How do you find the inverse of `log _ 1.25 (x)=y`?

Answer 1

See below

Explanation:

By definition of logarithm `log_1.25x=y hArr y^(1.25)=x`

But we know that `1.25=5/4`

`y^(5/4)=x` powering both sides to 4 we have

`(y^(5/cancel4))^cancel4=x^4`

`y^5=x^4` stracting 5th root

`root(5)(y^5)=y=root(5)(x^4)=x^(4/5)`