SOLUTION: express 2/3[ln(x^2-9)-ln(x+3)]+ln(x+4) as a single logarithm.
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Question 242310: express 2/3[ln(x^2-9)-ln(x+3)]+ln(x+4) as a single logarithm.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ -\ \ln\left(x-3\right)\right)\ +\ \ln\left(x+4\right))
The difference of the logs is the log of the quotient, that is:
 - \log_b(y) = log_b\left(\frac{x}{y}\right))
\right)\ +\ \ln\left(x+4\right))
\right)\ +\ \ln\left(x+4\right))
Use:
 = n\log_b(x))
^2}\right)\ +\ \ln\left(x+4\right))
The sum of the logs is the log of the product:
 + \log_b(y) = \log_b(xy))
^2}\right)\left(x+4\right)\right))
John
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