91Ó°ÊÓ

Find \(a\) so that the graph of \(f(x)=\log _{a} x\) contains the point (2,2)

Solve each exponential equation. Express irrational solutions in exact form. $$ e^{x+3}=\pi^{x} $$

Volume of a Cone The volume \(V\) of a right circular cone is \(V=\frac{1}{3} \pi r^{2} h .\) If the height is twice the radius, express the volume \(V\) as a function of \(r\)

Temperature Conversion The function \(C(F)=\frac{5}{9}(F-32)\) converts a temperature in degrees Fahrenheit, \(F\). to a temperature in degrees Celsius, \(C\). The function \(K(C)=C+273,\) converts a temperature in degrees Celsius to a temperature in kelvins, \(K\). (a) Find a function that converts a temperature in degrees Fahrenheit to a temperature in kelvins. (b) Determine 80 degrees Fahrenheit in kelvins.

Discounts The manufacturer of a computer is offering two discounts on last year's model computer. The first discount is a \(\$ 200\) rebate and the second discount is \(20 \%\) off the regular price, \(p\) (a) Write a function \(f\) that represents the sale price if only the rebate applies.(b) Write a function \(g\) that represents the sale price if only the \(20 \%\) discount applies. (c) Find \(f \circ g\) and \(g \circ f\). What does each of these functions represent? Which combination of discounts represents a better deal for the consumer? Why?

Write each expression as a single logarithm. \(3 \log _{5}(3 x+1)-2 \log _{5}(2 x-1)-\log _{5} x\)

If the average annual inflation rate is \(3.1 \%\), how long will it take for the CPI index to double?

Let \(f(x)=a x+b\) and \(g(x)=b x+a,\) where \(a\) and \(b\) are integers. If \(f(1)=8\) and \(f(g(20))-g(f(20))=-14\), find the product of \(a\) and \(b .^{*}\)

Use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. \(\log _{1 / 3} 71\)

Use the Change-of-Base Formula and a calculator to evaluate each logarithm. Round your answer to three decimal places. \(\log _{\sqrt{2}} 7\)