Find the values of the exponential functions \(f\) and \(g\), where \(f(x)=2^x\) and \(g(x)=3^x\), and \(x\in \{0,1,2,3,-2,-3\}\).

A patient is administered a \(1200\)-microgram dose of iodine-\(131\). How much iodine-\(131\) will be in the patient’s system after \(10\) days, after \(16\) days?

Sketch the graph of the exponential equation \(y=2^x\)

Sketch the graph of \(y=\left( \displaystyle\frac{1}{3} \right) ^x\)

You deposit \(\$500\) in an account that earns \(8\%\) compounded quarterly. Find an equation that gives the amount of money in the account after \(t\) years, the amount in the account after \(5\) years, and when it will contain \(\$1\text{,}000\).

Find the inverse of \(f(x)=2x-3\)

Graph \(y=x^2-2\) and find its inverse and graph it.

Find the inverse of \(g(x)=\displaystyle\frac{x-4}{x-2}\).

Graph \(y=2^x\) and its inverse \(x=2^y\)

Solve \(\log_3{x}=-2\)

Solve \(\log_x{4}=3\)

Solve \(\log_8{4}=x\)

Graph \(y=\log_2{x}\)

Simplify.

1. \(\log_2{8}\)

2. \(\log_{10}{10,000}\)

3. \(\log_b{b}\)

4. \(\log_b{1}\)

5. \(\log_4{\left(\log_5{5}\right)}\)

An earthquake has a magnitude of \(5\) on the Richter scale, what can we say about the size of its shock wave?

Expand \(\log_5{\left(\displaystyle\frac{3xy}{z}\right)}\)

Expand \(\log_2{\left(\displaystyle\frac{x^4}{\sqrt{y}\cdot z^3}\right)}\)

Simplify: \(2\log_{10}{a}+3\log_{10}{b}-\displaystyle\frac{1}{3}\log_{10}{c}\)

Solve \(\log_2{(x+2)}+\log_2{x}=3\)

Find \(\log{(2,760)}\)

Find \(\log{(0.0391)}\)

Find \(\log{(0.00523)}\)

Solve \(\log{x}=3.8774\)

Solve \(\log{x}=-2.4179\)

The San Francisco earthquake was \(8.3\) on the Richter scale. The San Fernando earthquake was measured \(6.6\). Find \(T\) for each and indicate how much stronger the San Francisco earthquake was.

Normal rainwater has a pH of \(5.6\). What is the concentration of hydrogen ions?

The concentration of hydrogen ions in acid rain known to kill fish is \(3.2 \times 10^{-5}\) moles per liter. Find the pH of this acid rain to the nearest tenth.

Simplify.

1. \(e^0\)

2. \(e^1\)

3. \(\ln e\)

4. \(\ln 1\)

5. \(\ln{e^3}\)

6. \(\ln{e^{-4}}\)

7. \(\ln{e^t}\)

Expand \(\ln{Ae^5t}\)

If \(\ln 2=0.6931\) and \(\ln 3=1.0986\), find

1. \(\ln 6\)

2. \(\ln 0.5\)

3. \(\ln 8\)

Solve \(25^{2x+1}=15\)

Find \(\log_8{24}\)

How long does it take \(\$5,000\) to double if it is in an account that yields \(5\%\) compounded once a year?

A city has a population of \(32\text{,}000\) in 1994. The population \(t\) years later can be estimated by \(P=32\text{,}000e^{0.05t}\). When will it have \(50\text{,}000\) people?