Question

If Logx (1 / 8) = - 3 / 2, then x is equal to a. - 4 b. 4 c. 1 / 4 d. 10

Answer 1

$log_x \frac{1}{8} = -\frac{3}{2} \\\\ which\ is \ the \is \ the \ same \ thing\ as \ saying\ \\\\x^ {-\frac{3}{2} }= \frac{1}{8} \\\\x^ {-\frac{3}{2} }= \frac{1}{2^3} \\\\x^ {-\frac{3}{2} }= 2^{-3} \\\\ x^ {-\frac{3}{2} }= 2^{-3*2* \frac{1}{2} } \\\\ x^ {-\frac{3}{2} }= ((2)^2)^{-3* \frac{1}{2} } \\\\ x^ {-\frac{3}{2} }= 4^{-\frac{3}{2} }$

Now,

Since the "x" and the "4" have the same exponent and they equal eachother,
x = 4