If 2 log x (3\(\frac{3}{8}\)) = 6, find the value of x
-
\(\frac{3}{2}\)
- \(\frac{4}{3}\)
- \(\frac{2}{3}\)
- \(\frac{1}{2}\)
The correct answer is: A
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 = \(\sqrt{\frac{27}{8}}\)
= (\(\frac{27}{8}\))\(\frac{1}{3}\)
= \(\frac{(3^3)^{\frac{1}{3}}}{(2^3)^{\frac{1}{3}}}\)
= \(\frac{3}{2}\)