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MATH 1314 LAB 6 F11

# MATH 1314 LAB 6 F11 - A Make sure all log terms are on one...

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MATH1314 LAB 6 NAME: ________________ Collin County College Fall 2011 Instructor: Daryl Rupp DUE 10/31/2010 Solving exponential equations with bases which are powers of the same number: A. Write both sides of the equation as powers of the same base. B. Set the exponents equal to each other. (b M = b N M = N) C. Solve for x. 1. 5 x 3 x 2 7 7 + + = 2. 9 1 3 13 x 5 = + Solving exponential equations with bases which are not powers of the same number: A. Isolate the exponential term, with a coefficient of one, on one side of the equation. B. Write the exponential equation as an equivalent logarithmic equation. ( M = b c log b M = c ) C. Solve for x. 3. 6 10 4 x = + 4. 8 + 2e x = 58 Solving exponential equations with bases which are not powers of the same number: A. Isolate the exponential term(s), with a coefficient of one. B. Take the “log” or “ln” of both sides. (M = N log b M = log b N) C. Simplify using the Power Rule. D. Solve for x. 5. 7 x+1 = 3 6. 5 x + 2 = 6 x – 7

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Solving logarithmic equations with log terms on only one side of the equation:
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Unformatted text preview: A. Make sure all log terms are on one side of the equation with non-log terms on the other side. B. Use the properties of logarithms to write all sums and differences as a single logarithm. C. Write the logarithmic equation as an equivalent exponential equation. ( log b M = c ↔ M = b c ) D. Solve for x. E. Check the proposed solutions in the original equation. 7. 4 ) 1 x ( log 2 =-+ 8. 2 ) 6 x ( log ) x ( log 4 4 =-+ Solving logarithmic equations with log terms with the same base on both sides of the equation: A. Use the properties of logarithms to write each side as a single logarithm. B. Set the arguments equal to each other. (log b M = log b N ↔ M = N) C. Solve for x. D. Check the proposed solutions in the original equation. 9. ) 15 ( ln ) 6 x ( ln 2 = + 10. ) 2 ( log ) 5 ( log ) x ( log 3 3 3 =-...
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