If 2 log x (3\(\frac{3}{8}\)) = 6, find the value of x

Explanation

2 log x (3\(\frac{3}{8}\)) = 6(divide both sides by 2)

\(\frac{2 log_x(3 \frac{3}{8})}{2} = \frac{6}{2}\)

\(\log_x \frac{27}{8} = 3\)

\(\frac{27}{8} = x^3\)

\(x^3 = \frac{27}{8}\)

x = \(\sqrt{\frac{27}{8}}\)

= (\(\frac{27}{8}\))^{\(\frac{1}{3}\)}

= \(\frac{(3^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}}\)

= \(\frac{3}{2}\)