91Ó°ÊÓ

Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility:$2^x×5={10}^x$

In Problems 41-52, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.

$f\left(x\right)=3^x-2$

Find the domain of the function.

$g\left(x\right)=\ln \left(\frac{1}{x+1}\right)$

Write each expression as a sum and/or difference of logarithms. Express powers as factors.

$\ln \frac{x}{e^x}$

The graph of a one-to-one function f is given. Draw the graph of the inverse function $f^{-1}$. For convenience (and as a hint), the graph of $y=x$is also given.

Price Appreciation of Homes

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

Solve each equation. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places. Verify your results using a graphing utility:${\log }_6(x+3)+{\log }_6(x+4)=1$

In Problems 41-52, use transformations to graph each function. Determine the domain, range, and horizontal asymptote of each function.

$f\left(x\right)=3^{x-1}$

In Problems 29 – 44, for the given functions f and g, find: (a) $f∘g$(b) $g∘f$(c) $f∘f$

(d) $g∘g$

State the domain of each composite function.

$f\left(x\right)=\frac{x-5}{x+1},g\left(x\right)=\frac{x+2}{x-3}$

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

${\left(\frac{3}{5}\right)}^x=7^{1-x}$