91Ó°ÊÓ

Evaluate each expression. Do not use a calculator. $$\log 10^{\sqrt{5}}$$

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\log (2-x)=0.5$$

Use the definition of inverse functions to show analytically that \(f\) and \(g\) are inverses. $$f(x)=3 x-7, \quad g(x)=\frac{x+7}{3}$$

In the formula \(A=P\left(1+\frac{r}{n}\right)^{n t},\) we can interpret \(P\) as the present value of A dollars t years from now, earning annual interest \(r\) compounded \(n\) times per year. In this context, \(A\) is called the future value. If we solve the formula for \(P,\) we obtain $$P=A\left(1+\frac{r}{n}\right)^{-n t}$$ Use the future value formula. Estimate the interest rate necessary for a present value of \(\$ 25,000\) to grow to a future value of \(\$ 30,416\) if interest is compounded annually for 5 years.

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\ln (1-x)=\frac{1}{2}$$

In the formula \(A=P\left(1+\frac{r}{n}\right)^{n t},\) we can interpret \(P\) as the present value of A dollars t years from now, earning annual interest \(r\) compounded \(n\) times per year. In this context, \(A\) is called the future value. If we solve the formula for \(P,\) we obtain $$P=A\left(1+\frac{r}{n}\right)^{-n t}$$ Use the future value formula. Estimate the interest rate necessary for a present value of \(\$ 1200\) to grow to a future value of \(\$ 1408\) if interest is compounded quarterly for 8 years.

Evaluate each expression. Do not use a calculator. $$\log 10^{\sqrt{3}}$$

Use the definition of inverse functions to show analytically that \(f\) and \(g\) are inverses. $$f(x)=4 x+3, \quad g(x)=\frac{x-3}{4}$$

Evaluate each expression. Do not use a calculator. $$\ln e^{2 / 3}$$

Graph each function. $$f(x)=\log _{5} x$$