Question

Find the exact value of the expression:4^log16^(7)A) ✓7B) 2✓3C) 8D) 49

Answer 1

Answer:

A) ✓7

Explanation:

Given the expression:

$4^{\log _{16}7}$

First, we can rewrite 4 as a root of 16.

$=16^{\frac{1}{2}\log _{16}7}$

Next, by the power law of logarithm:

$a\log x=\log x^a\implies\frac{1}{2}\log _{16}7=\log _{16}7^{\frac{1}{2}}$

Thus, our given expression becomes:

$=16^{\log _{16}\sqrt{7}}$

Using the logarithm property below:

$\begin{gathered} x^{\log _xa}=a \\ \implies16^{\log _{16}\sqrt[]{7}}=\sqrt[]{7} \end{gathered}$

The exact value of the expression is ✓7.

Option A is correct.