A solution has hydrogen ion concentration $3.2\times 10^{-5}$ moles per liter, where $\text{pH}=-\log [{\text{H}}^{+}]$. Find its pH to two decimal places.

For a solution with $[{\text{H}}^{+}]=6.3\times 10^{-8}$ moles per liter and $\text{pH}=-\log [{\text{H}}^{+}]$, find the pH to two decimal places.

A solution has $\text{pH}=2.75$, where $\text{pH}=-\log [{\text{H}}^{+}]$. Find $[{\text{H}}^{+}]$ to two significant figures in moles per liter.

A solution has $\text{pH}=5.60$, where $\text{pH}=-\log [{\text{H}}^{+}]$. Find $[{\text{H}}^{+}]$ to two significant figures in moles per liter.

A solution has $[{\text{H}}^{+}]=1.0\times 10^{-9}$ moles per liter, where $\text{pH}=-\log [{\text{H}}^{+}]$. Find its pH to two decimal places.

An earthquake of magnitude $7.1$ and one of magnitude $5.1$ are measured on the Richter scale. Each whole-number increase represents a factor of ten in intensity. How do their intensities compare?

Two earthquakes measure $4.8$ and $3.3$ on the Richter scale. If each whole step is a factor of ten in intensity, about how many times as intense is the first earthquake?

Earthquake A has Richter magnitude $6.0$ and earthquake B has magnitude $6.7$. Each whole-number increase is a factor of ten in intensity. How does B compare with A?

One earthquake measures $8.2$ on the Richter scale and another measures $5.2$. Each whole step is a factor of ten in intensity. How do their intensities compare?

A sound has intensity $I=3.2\times 10^{-7}$ watts per square meter. Use $L=10\log \left(\frac{I}{I_0}\right)$ with $I_0=10^{-12}$ watts per square meter. Find $L$ to two decimal places.

A sound has intensity $I=5.0\times 10^{-9}$ watts per square meter. Given $L=10\log \left(\frac{I}{I_0}\right)$ and $I_0=10^{-12}$ watts per square meter, find $L$ to two decimal places.

Using $L=10\log \left(\frac{I}{I_0}\right)$, a sound has $I=2.5\times 10^{-5}$ watts per square meter and $I_0=10^{-12}$ watts per square meter. Find $L$ to two decimal places.

A sound has intensity $I=8.0\times 10^{-11}$ watts per square meter. With $L=10\log \left(\frac{I}{I_0}\right)$ and $I_0=10^{-12}$ watts per square meter, find $L$ to two decimal places.

Solution A has pH $4$ and solution B has pH $7$. How do their hydrogen ion concentrations compare?

An earthquake changes from magnitude $5$ to magnitude $6$ on the Richter scale. What happens to its intensity?

Sound A is measured at $70$ decibels and sound B at $80$ decibels. How does the intensity of B compare with A?

Solution X has pH $2$ and solution Y has pH $3$. Which comparison is correct?

A machine produces a sound level of $65$ decibels. Given $L=10\log \left(\frac{I}{I_0}\right)$ and $I_0=10^{-12}$ watts per square meter, find $I$ to two significant figures.

A sound level is $42$ decibels. If $L=10\log \left(\frac{I}{I_0}\right)$ and $I_0=10^{-12}$ watts per square meter, find $I$ to two significant figures.

For a Richter model $M=\log \left(\frac{I}{I_0}\right)$, let $I_0=10^{-12}$ watts per square meter. An earthquake has $M=4.5$. Find its intensity $I$ to two significant figures.