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: 36

Answer

$\log_\sqrt{3}{9} = 4$

Work Step by Step

Let $\log_\sqrt{3}{9}=y$ RECALL: $\log_a{x} = y \longrightarrow a^y=x$ Use the rule above to obtain: $\log_\sqrt3{9} = y \longrightarrow (\sqrt{3})^y=9$ Write $9$ as $3^2$ to obtain: $(\sqrt{3})^y=3^2$ Note that $\sqrt{3} = 3^{\frac{1}{2}}$. Thus, the equation above is equivalent to: $(3^{\frac{1}{2}})^y = 3^2$ Use the rule $(a^m)^n=a^{mn}$ to obtain: $3^{\frac{1}{2} \cdot y} = 3^2 \\3^{\frac{y}{2}} = 3^2$ $\frac{y}{2} = 2$ Multiply $2$ to both sides of the equation to obtain: $2(\frac{y}{2}) = 2(2) \\y = 4$ Thus, $\log_\sqrt{3}{9} = 4$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.