Answer:
A) ✓7
Explanation:
Given the expression:
[tex]4^{\log _{16}7}[/tex]
First, we can rewrite 4 as a root of 16.
[tex]=16^{\frac{1}{2}\log _{16}7}[/tex]
Next, by the power law of logarithm:
[tex]a\log x=\log x^a\implies\frac{1}{2}\log _{16}7=\log _{16}7^{\frac{1}{2}}[/tex]
Thus, our given expression becomes:
[tex]=16^{\log _{16}\sqrt{7}}[/tex]
Using the logarithm property below:
[tex]\begin{gathered} x^{\log _xa}=a \\ \implies16^{\log _{16}\sqrt[]{7}}=\sqrt[]{7} \end{gathered}[/tex]
The exact value of the expression is ✓7.
Option A is correct.
