How would I solve for x if it's in an exponent?

Question

This is the problem. I'm stuck because it's in an exponent. I think I'd make the bases the same but I'm not sure where to go from there. 

 

8 ^ (6 · x − 7) = 64 ^ (7· x − 2)

 

also would I distribute the X (multiplication sign) like would it be 7x-2 or 7x-14 ? Thanks for any help!

Answer 1

With exponents, you want to have the same base on both sides of the equation if you can.

 

I.e. make the right side (8^2)^(7x - 2) and then 8^(14x-4).  Now you can just equate the left and right side exponent expressions.   6x-7 = 14x-4, and solve from there.