SOLUTION: Solve for x Log6(x) = log6(36) - log6(1/6) please explain and show work thanks

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Question 126569This question is from textbook Amscos Preparing for the Regents Examination Mathematics B
: Solve for x
Log6(x) = log6(36) - log6(1/6)
please explain and show work thanks This question is from textbook Amscos Preparing for the Regents Examination Mathematics B

Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Log%286%2Cx%29+=+log%286%2C36%29+-+log%286%2C1%2F6%29
In general, log%28a%2Fb%29+=+log%28a%29+-+log%28b%29
log%286%2Cx%29+=+log%286%2C36%2F%281%2F6%29%29
log%286%2Cx%29+=+log%286%2C216%29
Since these are equal, I can set each one equal to k
log%286%2Cx%29+=+k
log%286%2C216%29+=+k
6%5Ek+=+x
6%5Ek+=+216
x+=+216

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Log6(x) = log6(36) - log6(1/6)
Keep in mind that the base is 6 for all the work:
-------------------------
log(x) = log(36) - log(1/6)
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Rule: log(a)-log(b) = log(a/b)
-------------------------------
log(x) = log [36/(1/6)]
log(x) = log[216]
------------------------------
Since the logs are equal, the anti-logs are equal:
x = 216
==================
Another way to do it:
log6(x) = 2 -(-1)
log6(x) = 3
x = 6^3
x = 216
=============
Cheers,
Stan H.