Question

If Logx (1 / 8) = - 3 / 2, then x is equal to A. - 4 B. 4 C. 1 / 4

Answer 1

Answer:

B. 4

Step-by-step explanation:

Given :

$log_x(\frac{1}{8})=-\frac{3}{2}$

The logarithm function can be converted to an exponential function as

$[\log_ab=c]$ can be expressed as $[a^c=b]$

Similarly for the given expression

$log_x(\frac{1}{8})=-\frac{3}{2}$

We can write,

$x^{-\frac{3}{2}}=\frac{1}{8}$

Using property of negative exponents $[a^{-b}=\frac{1}{a^b}]$

$\frac{1}{x^{\frac{3}{2}}}=\frac{1}{8}$

So we can write that  as:

$x^{\frac{3}{2}}=8$

Writing the exponents in radical form as $a^{\frac{b}{c}}=(\sqrt[c]{a})^b$

$(\sqrt{x})^3=8$

Taking cube root both sides to remove the cube.

$\sqrt[3]{(\sqrt{x})^3}=\sqrt[3]{8}$

$\sqrt x=2$

Squaring both sides to remove square root.

$(\sqrt x)^2=2^2$

∴ $x=4$