SOLUTION: I need Help understanding how to do these: {{{log( 4, (x-2) )+log(4, (x-8) )= 2}}}

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Question 4396: I need Help understanding how to do these:
log%28+4%2C+%28x-2%29+%29%2Blog%284%2C+%28x-8%29+%29=+2
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
My obligatory cartoon:

Exponentiate both sides, that is, take 4 to the power of both sides:
log%28+4%2C+%28x-2%29+%29%2Blog%284%2C+%28x-8%29+%29=+2

4%5E%28log%28+4%2C+%28x-2%29+%29%2Blog%284%2C+%28x-8%29+%29%29=+4%5E2

%284%5Elog%28+4%2C+%28x-2%29+%29%29+%2A+%284%5Elog%284%2C+%28x-8%29+%29%29=+4%5E2

Note that a%5Elog%28a%2C+b%29+=+b, so 4%5Elog%28+4%2C+%28x-2%29+%29+=+x-2.

%28x-2%29%2A%28x-8%29+=+4%5E2+=+16
%28x-2%29%2A%28x-8%29+=+16
that simplifies to a simple quadratic equation, solve it. x=10 is one obvious answer, there could be another.