Explanation Given information: The equation, log 2 x + log 2 ( x − 15 ) = 4 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 Product property of logarithm: log b m + log b n = log b ( m ⋅ n ) Calculation: To solve the given logarithmic equation, first write the left side of equation by using the product rule of logarithm as shown log 2 x + log 2 ( x − 15 ) = 4 log 2 [ x ( x − 15 ) ] = 4 Now, write it in equivalent exponential formusing the logarithmic to exponential conversion property that log b x = y if and only if x = b y

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 17SP

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Solve the given equation log2x+log2(x−15)=4 for x.

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Chapter 2, Problem 16SP

Chapter 2, Problem 18SP

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Chapter 2 Solutions

Calculus

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Solve the given equation log 2 x + log 2 ( x − 15 ) = 4 for x.

Solution Summary: The author explains that if the same bases raised to different exponents are equal to each other, they will be equal as well.

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Solve the given equation log2x+log2(x−15)=4 for x.

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Chapter 2 Solutions