Solve the equation $3^{-x}=9.$

1. {2}

2. $\{-2\}$

3. $\left\{{\displaystyle \frac{1}{2}}\right\}$

4. $\left\{-{\displaystyle \frac{1}{2}}\right\}$

5. {ln 2}

Solve the equation ${\log }_{5}x=2.$

1. {10}

2. {25}

3. $\left\{{\displaystyle \frac{5}{2}}\right\}$

4. $\left\{{\displaystyle \frac{2}{5}}\right\}$

5. {2}

State the range and asymptote of $y=e^{-x}-1.$

1. $(0,\infty );y=-1$

2. $(-1,\infty );y=-1$

3. $(-\infty ,\infty );y=-1$

4. $(-1,\infty );y=1$

5. $(\infty ,1);y=1$

Evaluate ${\log }_{4}64.$

1. 16

2. 8

3. 2

4. 3

5. 4

Find the solution of the exponential equation ${\left({\displaystyle \frac{1}{3}}\right)}^{1-x}=3.$

1. $\left\{-{\displaystyle \frac{1}{3}}\right\}$

2. $\left\{{\displaystyle \frac{1}{3}}\right\}$

3. {1}

4. {2}

Evaluate log 0.01.

1. $-1.99999999$

2. $-2$

3. 2

4. 100

Which of the following expressions is equivalent to $\ln 7+2\ln x?$

1. $\ln (7+2x)$

2. $\ln (7x^2)$

3. ln (9x)

4. ln (14x)

Solve the equation $2^{x^2}=3^x.$

1. {0}

2. $\left\{{\displaystyle \frac{\ln 3}{\ln 2}}\right\}$

3. $\left\{0,{\displaystyle \frac{\ln 3}{\ln 2}}\right\}$

4. $\{0,\ln 3-\ln 2\}$

Solve the equation $e^{2x}-e^x-6=0.$

1. $\{-\ln 2\}$

2. $\{-\ln 3\}$

3. {ln 6}

4. {ln 3}

Rewrite the expression $\ln {\displaystyle \frac{3x^2}{{(x+1)}^{10}}}$ in expanded logarithmic form.

1. $\ln 6x-10\ln x+1$

2. $2\ln 3x-10\ln (x+1)$

3. $2\ln 3+2\ln x-10\ln (x+1)$

4. $\ln 3+2\ln x-10\ln (x+1)$

Find ${\ln e}^{3x}.$

1. 3

2. 3x

3. $3+x$

4. x

The equation for the graph obtained by shifting the graph of $y={\log }_{3}x$ 2 units up and 3 units left is

1. $y={\log }_3(x-3)+2.$

2. $y={\log }_3(x+3)-2.$

3. $y={\log }_3(x-3)-2.$

4. $y={\log }_3(x+3)+2.$

Find the domain of the function $f(x)=\ln (1-x)+3.$

1. $(-\infty ,1)$

2. $(1,\infty )$

3. $(-\infty ,-1)$

4. $(-\infty ,3)$

5. $(3,\infty )$

Write $\ln x-2\ln (x^2+1)+{\displaystyle \frac{1}{2}}\ln (x^4+1)$ in condensed form.

1. $\ln {\displaystyle \frac{x\sqrt{x^4+1}}{{(x^2+1)}^2}}$

2. $\ln {\displaystyle \frac{x}{x^2+1}}$

3. $\ln (x-{(x^2+1)}^2+{(x^4+1)}^{1/2})$

4. $2\ln {\displaystyle \frac{x(1+x^4)}{x^2+1}}$

Solve the equation $\log x=\log 12-\log (x+1).$

1. $\left\{{\displaystyle \frac{11}{2}}\right\}$

2. $\left\{{\displaystyle \frac{13}{2}}\right\}$

3. $\{3,-4\}$

4. {3}

5. $\left\{{\displaystyle \frac{2}{12}}\right\}$

Find x if ${\log }_{x}16=4.$

1. 4

2. 2

3. 64

4. ${\displaystyle \frac{1}{4}}$

5. 16

Suppose $12,000 is invested in a savings account paying 10.5% interest per year. Write the formula for the amount in the account after t years assuming that the interest is compounded monthly.

1. $A=12,000{(1.105)}^t$

2. $A=12,000{(1.525)}^{2t}$

3. $A=12,000{(1.2625)}^{4t}$

4. $A=12,000{(1.00875)}^{12t}$

The population of a certain city is growing according to the model $P=10,000{\log }_5(t+5),$ where t is time in years. If $t=0$ corresponds to the year 2000, what will the population of the city be in 2020?

1. 30,000

2. 20,000

3. 50,000

4. 10,000

Compare the intensity of the earthquake in 1994 in Northridge, California, of magnitude 6.7 to that of the 7.0 earthquake in 1988 in Armenia.

1. The Northridge earthquake was about twice as intense.

2. The Armenia earthquake was about twice as intense.

3. The Northridge earthquake was about a thousand times as intense.

4. The Armenia earthquake was about a thousand times as intense.