91Ó°ÊÓ

Evaluate the given quantities assuming that $$ \begin{array}{l} \log _{3} x=5.3 \text { and } \log _{3} y=2.1 \\ \log _{4} u=3.2 \text { and } \log _{4} v=1.3 \end{array} $$ $$ \log _{4} \frac{u}{8 v} $$

Find a formula for the inverse function \(f^{-1}\) of the indicated function \(f\). $$ f(x)=x^{1 / 7} $$

Suppose a bank account paying \(4 \%\) interest per year, compounded 12 times per year, contains \(\$ 10,555\) at the end of 10 years. What was the initial amount deposited in the bank account?

Evaluate the given quantities assuming that $$ \begin{array}{l} \log _{3} x=5.3 \text { and } \log _{3} y=2.1 \\ \log _{4} u=3.2 \text { and } \log _{4} v=1.3 \end{array} $$ $$ \log _{3} \sqrt{x} $$

For Exercises \(21-28,\) find a number \(b\) such that the indicated equality holds. $$ \log _{b} 64=3 $$

For Exercises \(21-28,\) find a number \(b\) such that the indicated equality holds.] $$ \log _{b} 64=6 $$

Evaluate the given quantities assuming that $$ \begin{array}{l} \log _{3} x=5.3 \text { and } \log _{3} y=2.1 \\ \log _{4} u=3.2 \text { and } \log _{4} v=1.3 \end{array} $$ $$ \log _{4} \sqrt{u} $$

Suppose a bank account paying \(6 \%\) interest per year, compounded four times per year, contains \(\$ 27,707\) at the end of 20 years. What was the initial amount deposited in the bank account?

Find a formula for the inverse function \(f^{-1}\) of the indicated function \(f\). $$ f(x)=x^{1 / 11} $$

Suppose a rock band is playing loudly at a sound level of 100 decibels. What decibel level would make the band sound three-fifths as loud?