SOLUTION: This one looked easy but it's got me confused please help and thank you. Use the laws of logarithms to express log base2 6 - log base 2 3 + 2 log base 2 sqrt8 as a single logarith

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: This one looked easy but it's got me confused please help and thank you. Use the laws of logarithms to express log base2 6 - log base 2 3 + 2 log base 2 sqrt8 as a single logarith      Log On


   

Question 280462: This one looked easy but it's got me confused please help and thank you.
Use the laws of logarithms to express log base2 6 - log base 2 3 + 2 log base 2 sqrt8 as a single logarithm then evaluate. I got this far log base 2^6 - log base2^3 +2 log base 2 sqrt 8 =log base 2 6/3 sqrt8^2??? help
Found 3 solutions by josmiceli, MathTherapy, greenestamps:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log%282%2C6%29+-+log%282%2C3%29+%2B+2%2Alog%282%2Csqrt%288%29%29
The 1st 2 terms are:
log%282%2C6%29+-+log%282%2C3%29+=+log%282%2C6%2F3%29
log%282%2C6%2F3%29+=+log%282%2C2%29
log%282%2C2%29+=+1
So far I have
1+%2B+2%2Alog%282%2Csqrt%288%29%29+=+1+%2B+log%282%2C%28sqrt%288%29%29%5E2%29
1+%2B+log%282%2C%28sqrt%288%29%29%5E2%29+=+1+%2B+log%282%2C8%29
1+%2B+log%282%2C8%29+=+1+%2B+3
1+%2B+3+=+4

Answer by MathTherapy(10704) About Me  (Show Source):
You can put this solution on YOUR website!
This one looked easy but it's got me confused please help and thank you.
Use the laws of logarithms to express log base2 6 - log base 2 3 + 2 log base 2 sqrt8 as a single logarithm
then evaluate. I got this far log base 2^6 - log base2^3 +2 log base 2 sqrt 8 =log base 2 6/3 sqrt8^2??? help
============================================================
log+%282%2C+%286%29%29+-+log+%282%2C+%283%29%29+%2B+2%2Alog+%282%2C+%28sqrt%288%29%29%29
log+%282%2C+%286%29%29+-+log+%282%2C+%283%29%29+%2B+log+%282%2C+%28sqrt%288%29%29%5E2%29
log+%282%2C+%286%29%29+-+log+%282%2C+%283%29%29+%2B+log+%282%2C+%288%29%29

Answer by greenestamps(13292) About Me  (Show Source):
You can put this solution on YOUR website!


You have done the harder part of the problem, using the laws of logarithms to write the given expression as a single logarithm. The rest of the problem is simple arithmetic, plus an application of the definition of logarithms:

6%2F3+=+2
%28sqrt%288%29%29%5E2=8
2%2A8=16

So you have

log%282%2C16%29

which is 4, because 2%5E4=16

ANSWER: 4