Question

How do you solve `6^x=72`?

Answer 1

`x≈2.387`

Explanation:

Using the `color(blue)"law of logarithms"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(logx^n=nlogx)color(white)(2/2)|)))`
`color(white)(xxxxxxx)"Applies to logs in any base."`

Take the natural log ( ln) of both sides.

`rArrln6^x=ln72`

Using the above law.

`xln6=ln72`

`rArrx=ln72/ln6≈2.387" to 3 decimal places"`