Question

convert log equation to exponential (numeric)
question
write the logarithmic equation as an exponential equation.
$log_{x}(sqrt{8})=\frac{3}{2}$

Explanation:

Step1: Recall log - exp conversion rule

The rule for converting $\log_{a}b = c$ to exponential form is $a^{c}=b$. In the given equation $\log_{x}(\sqrt{8})=\frac{3}{2}$, $a = x$, $b=\sqrt{8}$, and $c=\frac{3}{2}$.

Step2: Write in exponential form

So the exponential form is $x^{\frac{3}{2}}=\sqrt{8}$.

Answer:

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