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LAWS OF LOGARITHMS SECTION 5.6 Why do we need the Laws? To condense and expand logarithms: To Simplify! LAWS OF LOGARITHMS 1. log3 5 log3 x log3 5x When you are adding logs 2. multiply!! 9 log 4 9 log 4 x log 4 x When you are subtracting logs divide!! LAWS OF LOGARITHMS 3. log x 3log x 3 log x3 3log x LAWS OF LOGARITHMS 4. log5 x 5 x The log and exponential are inverses of each other so they cancel each other! Example: log3 2 x 3 2x e ln 5 5 LAWS OF LOGARITHMS 5. log8 8 x x This is because So we get And log8 8 x log8 8 log8 8 1 x Let’s Practice! (No Calculator) Evaluate log 3 log 6 log 5 2log12 6 log12 4 Let’s Practice! (No Calculator) Evaluate 1 log 64 2 log 5 3 Simplify e 1 ln x 2 Let’s Practice! (No Calculator) 3ln x e 1 ln 4 e Let’s Practice! (No Calculator) 10 4 log5 Express y in terms of x: log y 5log x Express y in terms of x: ln y 3ln x 2ln 6 Write as a single logarithm: 2 log8 x Solve: log7 x 8 log7 2 2 Solve: log 4 x 2 log 4 x log 4 8 2 Homework: 5.6 Page 200 1-45 every other odd