Question

How do you solve `15^(2x) = 36`?

Answer 1

`x~~0.66`

Explanation:

`1`. Since the left and right sides of the equation do not have the same base, start by taking the log of both sides.

`15^(2x)=36`

`log(15^(2x))=log(36)`

`2`. Use the log property, `log_color(purple)b(color(red)m^color(blue)n)=color(blue)n*log_color(purple)b(color(red)m)`, to simplify the left side of the equation.

`(2x)log15=log36`

`3`. Solve for `x`.

`2x=log36/log15`

`x=log36/(2log15)`

`color(green)(|bar(ul(color(white)(a/a)x~~0.66color(white)(a/a)|)))`