Question

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

Answer 1

A) ✓7

Explanation:

Given the expression:

`4^{\log _(16)7}`

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

`=16^{(1)/(2)\log _(16)7}`

Next, by the power law of logarithm:

`a\log x=\log x^a\implies(1)/(2)\log _(16)7=\log _(16)7^{(1)/(2)}`

Thus, our given expression becomes:

`=16^{\log _(16)√(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.