# Solve for x (1/3)^x = 724 Round your answer four decimals.

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### 2 Answers

To solve an equation containing a variable exponent, isolate the exponential quantity. Then take natural (to the base e) log on both sides.

`(1/3)^x = 724`

`rArr 3^-x=724`

`rArr -xln3=ln724`

`rArr x=-ln724/ln3`

`rArr x=-5.993746~~-5.9937`

**Therefore, the value of x is approximately -5.9937**.

(1/3)^x = 724

Here we have the x in the exponent. So we'll have to do the opposite operation of exponents which is log. Take the log of both sides:

log (1/3)^x = log724

A cool property of logs is that the exponent can now be written as multiplication like this:

x log(1/3) = log724

Remember that log of anything is just a number. So:

x = log724 / log(1/3)