91Ó°ÊÓ

For the following exercises, rewrite each equation in exponential form. $$\log _{\mathrm{a}}(b)=c$$

For the following exercises, use like bases to solve the exponential equation. $$ 2^{-3 n} \cdot \frac{1}{4}=2^{n+2} $$

For the following exercises, use the logistic growth model \(f(x)=\frac{150}{1+8 e^{-2 x}}\). Find and interpret \(f(0)\). Round to the nearest tenth.

The graph of \(f(x)=2\left(\frac{1}{4}\right)^{x-20}\) is shifted downward 4 units, and then shifted left 2 units, stretched vertically by a factor of 4 , and refl cted about the \(x\) -axis. What is the equation of the new function, \(g(x) ?\) State its \(y\) -intercept, domain, and range.

Use the logistic growth model \(f(x)=\frac{150}{1+8 e^{-2 x}}.\) Find and interpret \(f(0) .\) Round to the nearest tenth.

For the following exercises, identify whether the statement represents an exponential function. Explain. For each training session, a personal trainer charges his clients \(\$ 5\) less than the previous training session.

For the following exercises, state the domain and range of the function. $$h(x)=\ln \left(\frac{1}{2}-x\right)$$

The graph of \(f(x)=-\frac{1}{2}\left(\frac{1}{4}\right)^{x-2}+4\) is shifted downward 4 units, and then shifted left 2 units, stretched vertically by a factor of \(4,\) and reflected about the \(x\) -axis. What is the equation of the new function, \(g(x) ?\) State its \(y\) -intercept, domain, and range.

For the following exercises, state the domain and range of the function. $$g(x)=\log _{5}(2 x+9)-2$$

For the following exercises, expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. $$ \log _{2}\left(y^{x}\right) $$