Explanation Given information: The equation, 2 ln x − 1 2 ln 9 = ln 3 ( x − 2 ) Concept used: The equivalent exponential form of a logarithm for a > 0 , x > 0 , a ≠ 1 is given by log b x = y if and only if x = b y Exponent property of Equality : If the same bases raised to different exponents are equal to each other, then their exponents will be equal as well. That is, if a m = a n then m = n Exponent property, 1 a n = a − n Quotient property of logarithm: log b m − log b n = log b ( m n ) Power property of logarithm: n log b a = log b a n Calculation: To solve the given logarithmic equation, first write the left side of equation by using the power property and quotient property of logarithm as shown 2 ln x − 1 2 ln 9 = ln 3 ( x − 2 ) ln x 2 − ln 9 1 2 = ln 3 ( x − 2 ) ln x 2 − ln 3 = ln 3 ( x − 2 ) ln ( x

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 2, Problem 21SP

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Solve the given equation 2lnx−12ln9=ln3(x−2) for x.

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Chapter 2, Problem 20SP

Chapter 2, Problem 22SP

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Chapter 2 Solutions

Calculus

Ch. 2.1 - Prob. 1PS Ch. 2.1 - Prob. 2PS Ch. 2.1 - Prob. 3PS Ch. 2.1 - Prob. 4PS Ch. 2.1 - Prob. 5PS Ch. 2.1 - Prob. 6PS Ch. 2.1 - Prob. 7PS Ch. 2.1 - Prob. 8PS Ch. 2.1 - Prob. 9PS Ch. 2.1 - Prob. 10PS

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Solve the given equation 2 ln x − 1 2 ln 9 = ln 3 ( x − 2 ) for x.

Solution Summary: The author explains the equivalent exponential form of a logarithmic equation for x.

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Solve the given equation 2lnx−12ln9=ln3(x−2) for x.

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Chapter 2 Solutions