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`
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)