How to solve for x in exponent

Question

My problem is

(6^x)(6^-1)/6^7 = 6^7

Solve for X

I am just confused about how to solve for x. I try and get 6^x on its own, by having the equation 6^x = 6^15. If anyone can help me out, that would be great.

Answer 1

6^x 6^-1 / 6⁷ = 6⁷

6^x-1 = 6¹⁴

x - 1 = 14 So, x = 15

Answer 2

You're almost there!

6^x = 6¹⁵ is a correct simplification of your original equation - nice work.

The only step remaining is to recognize that both 6^x and 6¹⁵ share the same base of 6. Therefore, the only way these two expressions can be equal is if their exponents are equal.

What that means for us is that, simply, if 6^x = 6¹⁵, then x = 15.

To see why this is true, it might help to think of a simpler example, such as

2^x = 2³

We know 2³ = 2•2•2 = 8. So, this equation is equivalent to

2^x = 8

This equation is asking, 2 to what power equals 8? Wait...we just did that! We know 2³ = 8. So, our missing exponent x must be 3.