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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
log(2,8sqrt(2))

log%282%2C8sqrt%282%29%29

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log%282%2C2%5E3%2A2%5E%281%2F2%29%29
log%282%2C2%5E%283%261%2F2%29%29
log%282%2C2%5E%287%2F2%29%29
%287%2F2%29%2Alog%282%2C2%29
%287%2F2%29%2A1
highlight%287%2F2%29

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

log%282%2C%288%2Asqrt%282%29%29%29 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.
log%282%2C%288%2Asqrt%282%29%29%29+=+x

2%5Ex+=+8%2Asqrt%282%29 Convert the equation to exponential form

2%5Ex+=+2%5E3%2A%282%29%5E%281%2F2%29%5E%22%22 Rewrite 8 as 2^3. Rewrite the square root as an exponent of 1/2.

2%5E%28x%29+=+2%5E%283%2B1%2F2%29%5E%22%22 Use the rule that a^b*a^c = a^(b+c)

2%5E%28x%29+=+2%5E%287%2F2%29%5E%22%22

x+=+7%2F2 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