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Solution assignment 05 Logarithmic equations

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Assignment 5

Solve:

3\ln(x)+2\ln(x^2)=6

Solution

The domain of the function in the left-hand side is x>0.
We rewrite the equation:

3\ln(x)+4\ln(x)=6

7\ln(x)=6

\ln(x)=\displaystyle\frac{6}{7}

x=e^{\frac{6}{7}}

This solution lies in the domain and is valid.

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