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Unformatted text preview: Lesson_8.6_SolvingLogEqns.notebook 8.6 Solving Logarithmic Equations
To solve exponential equations, we can apply a logarithm to both sides of the equation. To solve logarithmic equations, we can rewrite the equation in exponential form, and then solve the resulting exponential equation. The following property is important when solving logarithmic equations:
• If logaM = logaN, then = (where a, M, and N > 0) Example #1: Solve each logarithmic equation.
(a) log6(x+ 5) = 2 (c) log4x = 2 log46 log43 (b) log3x = 3 log327 (d) log8x + log8(x + 2) = log88 Lesson_8.6_SolvingLogEqns.notebook
(e) 1 log(x 4) = log(x + 5) (f) log(x + 2) + log(2x 1) = 1 Lesson_8.6_SolvingLogEqns.notebook
Example #2: At a concert, the loudness of sound, L, in decibels, is given by the following equation, where I is the intensity, in watts per square metre, and I0 is the minimum intensity of sound audible to the average person (1.0 x 1012 W/m2). (a) The sound intensity at a concert is measured to be 0.9 W/m2. How loud is the concert? (b) On the way home from the concert, your car stereo produces 120 dB of sound. What is its intensity? Homework
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