Explanation Given: The expression is log ( 2 t + 3 ) + log ( 4 t − 1 ) = 2 log 3 . Formula used: For any positive real numbers M and N , and any positive base b ≠ 1 , the ratio formula of logarithm is, log b ( M N ) = log b M + log b N The power relation of logarithm is, log c ( M ) a = a log c M The logarithm, base b , of a positive number x is the power to which the base b must be raised to produce x . That is, 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 ( 2 t + 3 ) + log ( 4 t − 1 ) = 2 log 3 Use the property of product relation of the logarithm. log ( 2 t + 3 ) ( 4 t − 1 ) = 2 log 3 Use the property of power relation of the logarithm. log ( 2 t + 3 ) ( 4 t − 1 ) = log 3 2 log ( 8 t 2 − 2 t + 12 t − 3 ) = log 9 Solve further, 8 t 2 − 2 t + 12 t − 3 = 9 Subtract 9 from both the sides. 8 t 2 + 10 t − 3 − 9 = 0 8 t 2 + 10 t − 12 = 0 Factorize the equation. 8 t 2 + 16 t − 6 t − 12 = 0 Take common and further solve as, 8 t ( t + 2 ) − 6 ( t + 2 ) = 0 ( 8 t − 6 ) ( t + 2 ) = 0 t = − 2 , 3 4 Thus, the solutions come out to be − 2 , 3 4

8th Edition

ISBN: 9780134178967

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

Publisher: PEARSON

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Chapter 11, Problem 33RP

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To calculate: The value of t in the expression log(2t+3)+log(4t−1)=2log3 using properties of logarithms and check the answer.

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Chapter 11, Problem 32RP

Chapter 11, Problem 34RP

Chapter 11 Solutions

Intermediate Algebra (8th Edition)

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The value of t in the expression log ( 2 t + 3 ) + log ( 4 t − 1 ) = 2 log 3 using properties of logarithms and check the answer.

Solution Summary: The author calculates the value of t in the expression underset_34.

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To calculate: The value of t in the expression log(2t+3)+log(4t−1)=2log3 using properties of logarithms and check the answer.

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Chapter 11 Solutions