Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 4 - Review - Concept Check - Page 388: 10

Answer

Please see step-by-step.

Work Step by Step

a. A logarithmic equation is an equation in which the unknown (x) appears in the argument of a logarithm ( a logarithm of the variable occurs in the equation). b. Guidelines for Solving Exponential Equations can be found on p. 361: 1. Isolate the logarithmic term(s) on one side of the equation, and use the Laws of Logarithms to combine logarithmic terms if necessary. 2. Rewrite the equation in exponential form. 3. Solve for the variable. c. Applying the guidelines, 1. The term is isolated on the LHS. 2. LHS: Apply the law$\quad \log_{a}(A^{c})=C\log_{a}A$: $\log_{3}x^{4}=7$ .. now, write in exponential form, $\log_{3}x^{4}=7\Leftrightarrow 3^{7}=x^{4}$ 3.... solve for x... $x^{4}=3^{7}\qquad /(..)^{1/4}$ $ x=3^{7/4}\approx$ 6.83852117086
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