SOLUTION: 1. Write 4ln6-2ln3 as a single natural logarithm.
2. Solve e^3x=15
3. Simplify ln e^7
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Question 187548: 1. Write 4ln6-2ln3 as a single natural logarithm.
2. Solve e^3x=15
3. Simplify ln e^7
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Remember that
 = n\ln(x))
So:
-2\ln(3) = \ln(6^4) - \ln(3^2))
The difference of the logs is the log of the quotient, so:
 - \ln(3^2) = \ln (\frac{6^4}{3^2}) = \ln (\frac{2^4\,\cdot\,3^4}{3^2}) = \ln (2^4\,\cdot\,3^2) = \ln(16\,\cdot\,9)=\ln(144))
***************************************
Take the natural log of both sides:
 = \ln(15))
Use the exponent rule:
 = \ln(15))
 = 1)
so:
 \ \ \Rightarrow\ \ x = \frac{1}{3}\ln(15))
Leave your answer like that because it is much simpler than the only alternative, namely:
)
***************************************
Use the exponent rule:
 = 7 \ln(e) = 7)
John
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