Question

If 32^2C = 8^C+7, what is the value of c?
1
2
3
5

Answer 1

32 = 2⁵ and 8 = 2³, so you can rewrite the equation as

`32^(2c)=8^(c+7)\implies(2^5)^(2c)=(2^3)^(c+7)\implies 2^(10c)=2^(3c+21)`

The bases of both sides are equal, so the exponents must be too. Solve for c :

10c = 3c + 21

7c = 21

c = 3