SOLUTION: Write as a single logarithm {{{3logx-(1/2)log(x-2)+2log(x+5)^3}}} PLZ help I need tis as soon as possible

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Question 72874: Write as a single logarithm

PLZ help I need tis as soon as possible

Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
3logx-(1/2)log(x-2)+2log(x+5)^3
=logx^3 - log(x-2)^(1/2) + log(x+5)^2
=log[(x^3)(x+5)^2/(x-2)^(1/2)]
Cheers,
Stan H.

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
We're going to use these identities to rewrite the problem
1. Any number multiplied by a log can be placed as an exponent over the log's argument
2. The difference of two logs (with the same base) is equivalent to the log with 2 arguments divided.
3. The sum of two logs (with the same base) is equivalent to the log with 2 arguments multiplied.


Start with given problem.
Rewrite using identity 1. Place all numbers multiplying by the logs as exponents over their arguments.
Rewrite using identity 2. The second log is being subtracted from the first, so rewrite those two that makes the 1st number as the numerator and the 2nd as the denominator.
Rewrite using identity 3. Finish it up by multiplying the arguments of the logs that are being added.


This may seem like a lot if you've never seen these identities before, so feel free to ask further why I did a certain step. Hope this helps.

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