Question

Solve 15^2x = 36. Round to the nearest ten-thousandth.

Answer 1

There are a lot of ways you can go about this. One way is to take away the 2 from the exponent by squaring the 15, because exponent rules state that 15^2x is the same thing as (15^2)^x.

(15^2)^x = 225^x
225^x = 36

Now, you can take the log of both sides, with base 225 so that x is by itself.

Log225 (225)^x = Log225 (36)
x = Log225 (36)

You can either plug Log225 (36) straight into your calculator or if you can't do that, you can use the change of base formula to rewrite it as Log(36)/Log(225).

Log225 (36) = 0.6616