Question

If StartFraction 1 Over 64 EndFraction = 4 Superscript 2 s minus 1 Baseline times 16 Superscript 2 s + 2, what is the value of s?
–1
0
1
no solution

Answer 1

Convert to powers of 2:

1/64 = 2^{-6},
4^{2s-1} = (2^2)^{2s-1} = 2^{4s-2},
16^{2s+2} = (2^4)^{2s+2} = 2^{8s+8}.

Multiply: 2^{4s-2}·2^{8s+8} = 2^{12s+6}.

Set equal: 12s + 6 = -6 → 12s = -12 → s = -1.