Question

How do you solve `(1.5)^(3x)=7.5`?

Answer 1

`x~~1.66`

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.

`1.5^(3x)=7.5`

`log(1.5^(3x))=log(7.5)`

`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.

`(3x)log1.5=log7.5`

`3`. Solve for `x`.

`3x=log7.5/log1.5`

`x=log7.5/(3log1.5)`

`color(green)(|bar(ul(color(white)(a/a)x~~1.66color(white)(a/a)|)))`