Solving Logarithmic Equations Examples

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Solving logarithmic equations ck 12 foundation

Solving Logarithmic Equations CK 12 Foundation

Solve each of the following equations log4 x2 2x log4 5x 12 log 4 x 2 2 x log 4 5 x 12 Solution log 6x log 4 x log 3 log 6 x log 4 x log 3 Solution ln x ln x 3 ln 20 5x ln x ln x 3 ln 20 5 x Solution log3 25 x2 2 log 3 25 x 2 2 Solution We can solve exponential equations with base \(e\),by applying the natural logarithm of both sides because exponential and logarithmic functions are inverses of each other. See Example \(\PageIndex{6}\) and Example \(\PageIndex{7}\).

Solving logarithmic equations ck 12 foundation

Solving Logarithmic Equations CK 12 Foundation

Solving Logarithmic Equations ExamplesExample 1 Solve each of the following equations. \(2{\log _9}\left( {\sqrt x } \right) - {\log _9}\left( {6x - 1} \right) = 0\) \(\log x + \log \left( {x - 1} \right) = \log \left( {3x + 12} \right)\) \(\ln 10 - \ln \left( {7 - x} \right) = \ln x\) Show All Solutions Hide All Solutions Example 1 Solve log 2 5x 7 5 Solution Rewrite the equation to exponential form logs 2 5x 7 5 2 5 5x 7 32 5x 7 5x 32 7 5x 25 Divide both sides by 5 to get x 5 Example 2 Solve for x in log 5x 11 2 Solution Since the base of this equation is not given we therefore assume the base of 10