Find x if \(\frac{16^{2 + x}}{4} = 64^x\)

Explanation

\(\frac{16^{2 + x}}{4} = 64^x\)

16\(^{2 + x} = 4 \times 64^x\)

4\(^{2(2 + x)} = 4^1 \times 4^{3(x)}\)

(Equate coefficients since the bases are the same)

2(2 + x) = 1 + 3x

4 + 2x = 1 + 3x

2x - 3x = 1 - 4

-x = -3

x = 3.