Question

If you have an equation like
3 = (1 + x/12)^12
How do you solve for x ?
Like how do you get rid of that pesky exponent?

Answer 1

First, take the 12th root of both sides (raise both sides to the power of 1/12). Why? A property of exponents is that if you have a term with an exponent in it to another exponent, you multiply them together. Since words are confusing, here's an example:

(x^12)^(1/12) = x^(12 * 1/12) = x
(As you can see, I conveniently used 12 since your problem has an exponent of 12.

Going back to the problem after everything is raised to the power of 1/12, we have:
3^(1/12) = 1 + x/12

Doing basic algebra to arrive at the solution now:
(3^(1/12)) -1 = x/12
12((3^(1/12)) - 1 ) = x
x is equal to around 1.15.

Answer 2

thank you.. thats what I was missing.

I was thinking there must be some way to invert the ^12 on both sides, but wasn't clicking
thought it might require a log of some kind.

Answer 3

logs also work.

Answer 4

logs would make things more complicated.

Answer 5

If\[\Large x^n = a\]then take the nth root of both sides\[\Large x = \sqrt[n]{a}\]