Stitz-Zeager_College_Algebra_e-book

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Unformatted text preview: 8. We summarize the two common ways to solve log equations below. Steps for Solving an Equation involving Logarithmic Fuctions 1. Isolate the logarithmic function. 2. (a) If convenient, express both sides as logs with the same base and equate the arguments of the log functions. (b) Otherwise, rewrite the log equation as an exponential equation. Example 6.4.1. Solve the following equations. Check your solutions graphically using a calculator. 1. log117 (1 − 3x) = log117 x2 − 3 4. log7 (1 − 2x) = 1 − log7 (3 − x) 2. 2 − ln(x − 3) = 1 5. log2 (x + 3) = log2 (6 − x) + 3 3. log6 (x + 4) + log6 (3 − x) = 1 6. 1 + 2 log4 (x + 1) = 2 log2 (x) Solution. 1. Since we have the same base on both sides of the equation log117 (1 − 3x) = log117 x2 − 3 , we equate what’s inside the logs to get 1 − 3x = x2 − 3. Solving x2 + 3x − 4 = 0 gives x = −4 and x = 1. To check these answers using the calculator, we make use of the change ln(x2 −3) of base formula and graph f (x) = ln(1−3x) and g (x) = ln(117) and we se...
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