SOLUTION: writing an expression as a single logarithm {{{5(ln x + ln 7) - 3(ln x+ ln 5)}}}

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Question 541556: writing an expression as a single logarithm 5%28ln+x+%2B+ln+7%29+-+3%28ln+x%2B+ln+5%29
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
5%2A%28lnx%2Bln7%29-3%2A%28lnx%2Bln5%29 Apply the distributive property to both terms.
%285%2Alnx%2B5%2Aln7%29-%283%2Alnx%2B3%2Aln5%29 Now apply the "power rule" for logarithms.
%28lnx%5E5%2Bln7%5E5%29-%28lnx%5E3%2Bln5%5E3%29 Now apply the "product rule".
ln%28x%5E5%2A7%5E5%29-ln%28x%5E3%2A5%5E3%29 Simplify using: 7%5E5+=+16807 and 5%5E3+=+125.
ln%2816807x%5E5%29-ln%28125x%5E3%29 Now apply the "quotient rule".
ln%2816807x%5E5%2F125x%5E3%29 Simplify.
ln%28134.456x%5E2%29