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### Section 6.4 : Solving Logarithm Equations

Solve each of the following equations.

1. $${\log _4}\left( {{x^2} - 2x} \right) = {\log _4}\left( {5x - 12} \right)$$ Solution
2. $$\log \left( {6x} \right) - \log \left( {4 - x} \right) = \log \left( 3 \right)$$ Solution
3. $$\ln \left( x \right) + \ln \left( {x + 3} \right) = \ln \left( {20 - 5x} \right)$$ Solution
4. $${\log _3}\left( {25 - {x^2}} \right) = 2$$ Solution
5. $${\log _2}\left( {x + 1} \right) - {\log _2}\left( {2 - x} \right) = 3$$ Solution
6. $${\log _4}\left( { - x} \right) + {\log _4}\left( {6 - x} \right) = 2$$ Solution
7. $$\log \left( x \right) = 2 - \log \left( {x - 21} \right)$$ Solution
8. $$\ln \left( {x - 1} \right) = 1 + \ln \left( {3x + 2} \right)$$ Solution
9. $$2\log \left( x \right) - \log \left( {7x - 1} \right) = 0$$ Solution