Explanation Given: The equation is log 8 ( x − 3 ) = − 1 + log 8 6 x . Formula used: For any positive real numbers M and N , and any positive base c ≠ 1 , the ratio formula of logarithm is, log c ( M N ) = log c ( M ) − log c ( N ) . The logarithm, base b , of a positive number x is the power to which the base b must be raised to produce x . y = log b x is the same as x = b y , where b > 0 and b ≠ 1 and y and x are arbitrary constants. Calculation: Consider the expression, log 8 ( x − 3 ) = − 1 + log 8 6 x Rearrange the equation. log 8 ( x − 3 ) − log 8 6 x = − 1 Use the logarithm property for ratio relation. log 8 ( x − 3 6 x ) = − 1 Convert into exponential form. ( x − 3 6 x ) = 8 − 1 ( x − 3 6 x ) = 1 8 x − 3 = 6 x ( 1 8 ) Further solve as, x − 3 = 3 x 4 Add 3 and subtract 3 x 4 both the sides

8th Edition

ISBN: 9780134178967

Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford

Publisher: PEARSON

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Chapter 11, Problem 32RP

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To calculate: The value of x in the equation log8(x−3)=−1+log86x by using the properties of logarithms and check the answer.

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Chapter 11, Problem 31RP

Chapter 11, Problem 33RP

Chapter 11 Solutions

Intermediate Algebra (8th Edition)

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The value of x in the equation log 8 ( x − 3 ) = − 1 + log 8 6 x by using the properties of logarithms and check the answer.

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To calculate: The value of x in the equation log8(x−3)=−1+log86x by using the properties of logarithms and check the answer.

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Chapter 11 Solutions