Question

Write the given statement in an equivalent exponential form.log 216 = 8V2The equivalent exponential form of the given statement is(Type your answer using exponential notation. Do not simplify.)

Answer 1

We can rewrite the square root as :

$\sqrt[]{a}=a^{\frac{1}{2}}$

Then:

$\log _{2^{\frac{1}{2}^{}}}16=8$

Use the next property:

$\log _ax=y\text{ is equal to }a^y=x$

Where a=2^(1/2), x=16 and y=8

Then:

$\log _{2^{\frac{1}{2}^{}}}16=8\text{ is equal to (}2^{\frac{1}{2}})^8=16$

Simplify the expression:

$\text{(}2^{\frac{1}{2}})^8=2^4^{}$

Then:

$2^4=16$