Question

How do you solve `3^x-2=11`?

Answer 1

`x≈2.335`

Explanation:

We use the `color(blue)"law of logarithms"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(a/a)color(black)(logx^n=nlogx)color(white)(a/a)|)))`

`3^x-2=11rArr3^x=13`

Now take the ln of both sides. I have used ln but a log to any base can be used.

`rArrln3^x=ln13`

Using the above law allows us to obtain x as a multiplier.

`xln3=ln13rArrx=(ln13)/(ln3)≈2.335`