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SOLVING LOGARITHMIC EQUATIONS A logarithmic equation can be solved by expressing it in exponential form and solving the resulting exponential equation. Recall… y = logax is only defined for x > 0 Therefore, when solving log equations, answers where x 0 are inadmissible. Example Solve each of the following: a) 1 log x 2 25 b) log6(2x – 1) = log69 c) log23 + log2x = log218 d) log324x – log38 = 4 e) log427 = 3log4x f) log2(x + 2) + log2(x – 1) = 2 A solution is inadmissible if its substitution in the original equation results in an undefined value!! Summary When solving a logarithmic equation: Example simplify using the laws of logarithms if logaM = logaN, then M = N, where a, M, N > 0 check for inadmissible solutions A Richter scale is used to compare the intensities of earthquakes. The Richter scale magnitude, R, of an earthquake is determined using the given equation, where a is the amplitude of the vertical ground motion in microns (), T is the period of the seismic wave in seconds, and B is a factor that accounts for the weakening of the seismic waves. An earthquake measured 5.5 on the Richter scale, and the period of the seismic wave was 1.8s. If B equals 3.2, determine the amplitude of the vertical ground motion. a R log B T Note: 1 = 10–6 m Homework: p.491–492 #1–7, 10, 17, 19