Algebra 2 value of x

Question

If 3^{2x - 2} = 81, what is the value of x?

(a) 1

(b) 2

(c) 3

(d) 4

Answer 1

3^2x-2 = 3⁴

So what is the value of x?

Answer 2

If you have a strong grasp of basic multiplication facts, then you would recall that 81 = 3⁴.

With that we can re-write the problem as 3^{2x - 2} = 3⁴.

From this we can see that the only real "work" here is 2x - 2 = 4.

Do I need to continue??

Ok, I will.

2x = 4 + 2

2x = 6

x = 3

The answer is...c.

:)