SOLUTION: I cannot figure out how to rewrite this logarithm as one simplified logarithm log(6x)+5log(3x)-3log(9x) Please help. xandra

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Question 131451: I cannot figure out how to rewrite this logarithm as one simplified logarithm
log(6x)+5log(3x)-3log(9x)
Please help.
xandra
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
I cannot figure out how to rewrite this logarithm as one simplified logarithm
log(6x)+5log(3x)-3log(9x)
Please help. 

log%28%286x%29%29%2B5log%28%283x%29%29-3log%28%289x%29%29

Use a rule of logs to write the coefficients as exponents:

log%28%286x%29%29%2Blog%28%283x%29%5E5%29-log%28%289x%29%5E3%29

Use a law of exponents to remove the inner parenthesesL:

log%28%286x%29%29%2Blog%28%283%5E5x%5E5%29%29-log%28%289%5E3x%5E3%29%29

Use a rule of logs on the first two terms:

log%28%286x%2A3%5E5%2Ax%5E5%29%29-log%28%289%5E3x%5E3%29%29

Write 6 as 2%2A3 and 9 as 3%5E2

log%28%282%2A3%2Ax%2A3%5E5%2Ax%5E5%29%29-log%28%28%283%5E2%29%5E3x%5E3%29%29

Add exponents of 3 and x in the first term and multiply
exponents in the second term:

+log%28%282%2A3%5E6%2Ax%5E6%29%29-log%28%283%5E6x%5E3%29%29

Use a rule of logs:

log%28%28+%282%2A3%5E6%2Ax%5E6%29%2F%283%5E6x%5E3%29++%29+++++%29

 Cancel the 3%5E6's

log%28%28+%282%2Across%283%5E6%29%2Ax%5E6%29%2F%28cross%283%5E6%29x%5E3%29++%29+++++%29

log%28%28+%282%2Ax%5E6%29%2F%28x%5E3%29++%29+++++%29

Subtract the exponents of the x's

log%28+%282x%5E3%29++%29+++++

Edwin