Solve the equation $5^{-x}=125.$

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

State the range of $y=-e^x+1$ and find the asymptote of its graph.

Evaluate ${\log }_2{\displaystyle \frac{1}{8}}.$

Solve the exponential equation ${\left({\displaystyle \frac{1}{4}}\right)}^{2-x}=4.$

Evaluate log 0.001 without using a calculator.

Rewrite the expression $\ln 3+5\ln x$ in condensed form.

Solve the equation $2^{x+1}=5.$

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

Rewrite the expression $\ln {\displaystyle \frac{2x^3}{{(x+1)}^5}}$ in expanded logarithmic form.

Evaluate ${\ln e}^{-5}.$

Give the equation for the graph obtained by shifting the graph of $y=\ln x$ up 3 units and 1 unit right.

Sketch the graph of $y=3^{x-1}+2.$

State the domain of the function $f(x)=\ln (-x)+4.$

Write $3\ln x+\ln (x^3+2)-{\displaystyle \frac{1}{2}}\ln (3x^2+2)$ in condensed form. 

Solve the equation $\log x=\log 6-\log (x-1).$

Find x if ${\log }_{x}9=2.$

Suppose $15,000 is invested in a savings account paying 7% interest per year. Write the formula for the amount in the account after t years if the interest is compounded quarterly.

Suppose the number of Hispanic people living in the United States is approximated by $\text{H}=15,000e^{0.2t},$ where $t=0$ represents 1960. According to this model, in which year did the Hispanic population in the United States reach 1.5 million?

Compare the intensity of the earthquake in 1960 in Morocco of magnitude 5.8 to that of the 6.2 magnitude earthquake in 1972 in Nicaragua.