91Ó°ÊÓ

For the following exercises, evaluate the common logarithmic expression without using a calculator. $$2 \log \left(100^{-3}\right)$$

For the following exercises, use a graphing calculator to approximate the solutions of the equation. Round to the nearest thousandth. \(f(x)=a b^{x}+d\). $$ 5=3\left(\frac{1}{2}\right)^{x-1}-2 $$

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary. $$f(x)=1.2 e^{2 x}-0.3, \text { for } f(3)$$

For the following exercises, evaluate the natural logarithmic expression without using a calculator. $$\ln \left(e^{\frac{1}{3}}\right)$$

For the following exercises, solve each equation for \(x\). $$ \log _{3}(3 x)-\log _{3}(6)=\log _{3}(77) $$

For the following exercises, use a graphing calculator to approximate the solutions of the equation. Round to the nearest thousandth. \(f(x)=a b^{x}+d\). $$ -30=-4(2)^{x+2}+2 $$

For the following exercises, use this scenario: The equation \(N(t)=\frac{500}{1+49 e^{-0.7 t}}\) models the number of people in a town who have heard a rumor after \(t\) days. How many people started the rumor?

For the following exercises, evaluate each function. Round answers to four decimal places, if necessary. $$f(x)=-\frac{3}{2}(3)^{-x}+\frac{3}{2}, \text { for } f(2)$$

Explore and discuss the graphs of \(f(x)=(b)^{x}\) and \(g(x)=\left(\frac{1}{b}\right)^{x} .\) Then make a conjecture about the relationship between the graphs of the functions \(b^{x}\) and \(\left(\frac{1}{b}\right)^{x}\) for any real number \(b>0\).

For the following exercises, evaluate the natural logarithmic expression without using a calculator. $$\ln (1)$$