Question

How do i solve 36^5x= (6^x)(6^x-2)

Answer 1

You need to get a common base. In this question, your bases are 36, 6, 6. Use a base of 6 (and hence change 36 to 6).

36 = 6^2
36^5x = 6^2(5x)
= 6^10x

Your equation now is:
6^10x = 6^(x+x-2) INDEX LAWS

Since we have the same base, the powers must be equal:
10x = x+x-2
8x = -2
x = -1/4