91Ó°ÊÓ

Solve each logarithmic equation. Express irrational solutions in exact form. $$ \log (x-1)=\frac{1}{3} \log 2 $$

Find the domain of each function. $$ H(x)=\log _{5} x^{3} $$

Find the domain of each function. $$ f(x)=3-2 \log _{4}\left(\frac{x}{2}-5\right) $$

The function \(f\) is one-to-one. (a) Find its inverse function \(f^{-1}\) and check your answer. (b) Find the domain and the range of \(f\) and \(f^{-1}\). (c) Graph \(f, f^{-1},\) and \(y=x\) on the same coordinate axes. $$ f(x)=3 x $$

Write each expression as a sum and/or difference of logarithms. Express powers as factors. \(\ln \frac{x}{e^{x}}\)

Show that \((f \circ g)(x)=(g \circ f)(x)=x\) \(f(x)=9 x-6 ; \quad g(x)=\frac{1}{9}(x+6)\)

What will a $$ 90,000\( condominium cost 5 years from now if the price appreciation for condos over that period averages \)3 \%$ compounded annually?

A department store charges \(1.25 \%\) per month on the unpaid balance for customers with charge accounts (interest is compounded monthly). A customer charges \(\$ 200\) and does not pay her bill for 6 months. What is the bill at that time?

Find the domain of each function. $$ g(x)=8+5 \ln (2 x+3) $$

The function \(f\) is one-to-one. (a) Find its inverse function \(f^{-1}\) and check your answer. (b) Find the domain and the range of \(f\) and \(f^{-1}\). (c) Graph \(f, f^{-1},\) and \(y=x\) on the same coordinate axes. $$ f(x)=-4 x $$