Question

How do you solve `5^x = 28`?

Answer 1

`x~~2.07`

Explanation:

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

`5^x=28`

`log(5^x)=log(28)`

`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.

`xlog(5)=log(28)`

`3`. Solve for `x`.

`x=(log(28))/(log(5))`

`color(green)(|bar(ul(color(white)(a/a)x~~2.07color(white)(a/a)|)))`