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

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

A.

$\frac{3}{2}$

B.

$\frac{4}{3}$

C.

$\frac{2}{3}$

D.

$\frac{1}{2}$

View answer & explanation

Correct answer is A

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 = $\sqrt{\frac{27}{8}}$

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

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

= $\frac{3}{2}$

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