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^{(1)/(2)}`

Then:

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

Simplify the expression:

`\text{(}2^{(1)/(2)})^8=2^4^{}`

Then:

`2^4=16`