SOLUTION: what is the product of 2 log x = log 8? I hope you could give me an exact answer, and thanks for your help.

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Question 319899: what is the product of 2 log x = log 8?
I hope you could give me an exact answer, and thanks for your help.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
A general rule is:
log%28a%5Eb%29+=+b%2Alog%28a%29
Using the right to left version of the rule,
2%2Alog%28x%29+=+log%28x%5E2%29, so
log%28x%5E2%29+=+log%288%29
If the logs are equal, the numbers are equal
x%5E2+=+8
x+=+sqrt%288%29
x+=+2.828
I can check this:
2%2Alog%28x%29+=+log%288%29
2%2Alog%282.828%29+=+log%288%29
2%2A.4515+=+.9031
.903+=+.9031 slight round-off error