College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding: 94

Answer

$x=\dfrac{1}{2}$

Work Step by Step

RECALL: $\log_a{x} = y \longrightarrow a^y=x, a\gt0, a\ne 1$ Use the definition above to obtain: $\log_x{(\frac{1}{8})}=3 \\ \longrightarrow x^3=\frac{1}{8} \\x^3 = \frac{1}{2^3} \\x^3=(\frac{1}{2})^3$ Take the cube root of both sides to obtain: $x = \sqrt[3]{(\frac{1}{2})^3}$ Use the rule $\sqrt[3]{a^3} = a$ to obtain: $x = \frac{1}{2}$
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