Question

If `5^-x = 1/3`, then what is the value of `25^x`?

Answer 1

`~~8.92`

Explanation:

First solve for x

`1/5^× = 1/3`
`5^× = 3`
`xlog(5) =log(3)`
`×=log(3)/log(5)~~.68`
Therefore
`25^× ~~8.92`

So the only part I want to emphasize is the log operation. Log is a nice way to change multiplication and division into addition and subtraction. Another benefit is that any power becomes a multiple. Uaing it allowed me to bring x down and then solve more simply.

Answer 2

`9`

Explanation:

Alternate way of doing it.

We know that `25 = 5^2`, thus `25^x= (5^2)^x = 5^(2x) = (5^x)^2`

We know from the first equation that `1/5^x = 1/3`, because `a^-n = 1/a^n`.

This means that `5^x = 3`. We rewrote `25^x` as `(5^x)^2` above so now we can substitute.

`(5^x)^2 = 3^2 = 9`

Hopefully this helps!