Question

1 over the square root of 8 = 4^(m − 2)?

Answer 1

Answer:

5.5

Step-by-step explanation:

$\frac{1}{ \sqrt{8} } = {4}^{(m - 2)}$

Squaring both sides

$\frac{1}{8} = {4}^{2(m - 2)} \\ \frac{1}{8} = {4}^{2} \times {4}^{(m - 2)} \\ \frac{1}{8 \times {4}^{2} } = {4}^{(m - 2)} \\ \frac{1}{8 \times 16} = {4}^{(m - 2)} \\ \frac{1}{128} = {4}^{(m - 2)} \\ log_{4}(128) = (m - 2) \\ \frac{7}{2} = m - 2 \\ m = \frac{11}{2} = 5.5$