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Section 6.4 : Solving Logarithm Equations

Solve each of the following equations.

1. \({\log _{11}}\left( {{x^2} + 3x} \right) = {\log _{11}}\left( {3x + 16} \right)\)
2. \(\ln \left( {4 - 3x} \right) - \ln \left( {7x} \right) = \ln \left( {11} \right)\)
3. \(log\left( x \right) + \log \left( {x + 12} \right) = \log \left( {x - 10} \right)\)
4. \(\ln \left( x \right) = \ln \left( {15 - x} \right) - \ln \left( {x + 1} \right)\)
5. \({\log _8}\left( {4x + 1} \right) = - 1\)
6. \({\log _6}\left( {3x} \right) - {\log _6}\left( {x + 5} \right) = 1\)
7. \({\log _3}\left( x \right) + {\log _3}\left( {x + 6} \right) = 3\)
8. \({\log _2}\left( {{x^2}} \right) = 2 + {\log _2}\left( {8 - x} \right)\)
9. \({\log _4}\left( x \right) = 2 - {\log _4}\left( {x + 6} \right)\)
10. \(\log \left( { - x} \right) + \log \left( {15 - x} \right) = 2\)
11. \(\ln \left( x \right) + \ln \left( {x - 2} \right) = 3\)
12. \(2\log \left( x \right) - \log \left( {{x^2} + 4x + 1} \right) = 0\)