Question

If `log_4x=2.5` and `log_y125=-3/2`, what is the numerical value of `x/y` in simplest form?

Answer 1

I found: `x/y=800`

Explanation:

We can first write (using the definition of log):

`x=4^(2.5)=4^(5/2)=root2(4^5)=32`
and:
`125=y^(-3/2)`
or (raising both sides to `-2/3`):
`125^(-2/3)=y^((-3/2)(-2/3))`
`y=125^(-2/3)`

Then we divide to find:

`x/y=32/125^(-2/3)`

or rearranging:

`x/y=32*125^(2/3)`
`x/y=32*root3(125^2)`
`x/y=32*25`
`x/y=800`