A semi-log plot of $\log y$ against $x$ is a straight line with slope $-1$ passing through $(0,-2)$. Which model does that recover?

A semi-log plot of $\log y$ against $x$ is a straight line with slope $-2$ passing through $(0,-3)$. Which model does that recover?

Solve $\log (x-8)+\log (x-7)=\log 6$, giving only the solutions the logarithms allow.

On the Richter scale, one earthquake measures $6$ and another measures $3$. How many times greater is the seismic wave amplitude of the first than the second?

Solve $\log (x-1)+\log (x-2)=\log 6$, giving only the solutions the logarithms allow.

Write $3\log x+2\log y-2\log z$ as a single logarithm.

Write $4\log x+\log y-2\log z$ as a single logarithm.

Solve ${\log }_{6}x=2$ for $x$.

Over five equally spaced readings, the value of a machine measures 5, 8, 11, 14 and 17 dollars, one reading per year. Which model reproduces the record?

Over five equally spaced readings, a savings balance measures 3, 8, 13, 18 and 23 dollars, one reading per year. Which model reproduces the record?

One measurement has $100000$ times the hydrogen ion concentration of another. By how much do their readings on the pH scale differ?

Solve $2{\left(10\right)}^x=200$ for $x$.

Write $\log x+2\log y-\log z$ as a single logarithm.

On the Richter scale, one earthquake measures $7$ and another measures $2$. How many times greater is the seismic wave amplitude of the first than the second?

A semi-log plot of $\log y$ against $x$ is a straight line with slope $1$ passing through $(0,0)$. Which model does that recover?

Solve ${\log }_{10}x=4$ for $x$.

Solve ${\log }_{5}x=3$ for $x$.

Solve ${\log }_{2}x=3$ for $x$.

Write $3\log x+\log y-2\log z$ as a single logarithm.

A semi-log plot of $\log y$ against $x$ is a straight line with slope $1$ passing through $(0,3)$. Which model does that recover?

Solve ${\log }_{4}x=3$ for $x$.

On the Richter scale, one earthquake measures $5$ and another measures $3$. How many times greater is the seismic wave amplitude of the first than the second?

Over five equally spaced readings, the number of cells in a lab culture measures 8, 24, 72, 216 and 648, one reading per hour. Which model reproduces the record?

A semi-log plot of $\log y$ against $x$ is a straight line with slope $-3$ passing through $(0,1)$. Which model does that recover?

Write $4\log x+\log y-3\log z$ as a single logarithm.

Over five equally spaced readings, the area of a spreading stain measures 6, 10, 14, 18 and 22 square centimeters, one reading per minute. Which model reproduces the record?

Solve $\log (x-3)+\log (x-2)=\log 2$, giving only the solutions the logarithms allow.

On the decibel scale, one sound measures $60$ dB and another measures $20$ dB. How many times greater is the sound intensity of the first than the second?

Solve $\log (x-6)+\log (x-8)=\log 15$, giving only the solutions the logarithms allow.

Over five equally spaced readings, the area of a spreading stain measures 10, 12, 14, 16 and 18 square centimeters, one reading per minute. Which model reproduces the record?