SOLUTION: Sorry I don't know how to type this up. I looked at the guide but still can't get it right. Evaluate. https://i.ibb.co/sJncj5q/1.jpg

Question 1204567: Sorry I don't know how to type this up. I looked at the guide but still can't get it right.
Evaluate.
https://i.ibb.co/sJncj5q/1.jpg
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
log(2,8sqrt(2))

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Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

would be written out as log(2, 8*sqrt(2) )
Or you could say "log base 2 of 8*sqrt(2)"

Here is one approach.

Convert the equation to exponential form

Rewrite 8 as 2^3. Rewrite the square root as an exponent of 1/2.

Use the rule that a^b*a^c = a^(b+c)

Since the bases are equal, the exponents must be equal.

Another approach would be to use the change of base formula similar to what was done on this question
https://www.algebra.com/algebra/homework/logarithm/logarithm.faq.question.1204568.html

As quick confirmation, use a calculator to find that
log( 8*sqrt(2) )/log(2) = 3.5
and
7/2 = 3.5

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