Question

simplify the expression without using a calculator.
$10^{log sqrt3{6x}}$

$10^{log sqrt3{6x}} = \square$
(type an exact answer using radicals as needed.)

Explanation:

Step1: Recall the inverse property of logarithms

For the exponential function \( y = 10^{\log a} \), by the inverse property of logarithms (where the base of the exponential and the base of the logarithm are the same, here base 10), we know that \( 10^{\log a}=a \) for \( a>0 \).

Step2: Apply the property to the given expression

In the given expression \( 10^{\log\sqrt[3]{6x}} \), let \( a = \sqrt[3]{6x} \). Then using the inverse property \( 10^{\log a}=a \), we substitute \( a=\sqrt[3]{6x} \) into the formula.

Answer:

\(\sqrt[3]{6x}\)