Question

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

Answer 1

32^{2c} = 8^{c+7}

Write both bases as powers of 2: 32 = 2^5, 8 = 2^3.

(2^5)^{2c} = (2^3)^{c+7} → 2^{10c} = 2^{3c+21}.

So 10c = 3c + 21 → 7c = 21 → c = 3.

Answer: 3.