Mastery Check Solutions

Show What You Know

If $\log_{a} b = y$ , prove $\log_{a} b = \frac{\log b}{\log a}$ .

Explain the steps you used in part A. Write them beside each step.

$\begin{matrix} a^{y} = b & Log to exponential equation \\ \log a^{y} = \log b & Equality Rule for common logs \\ y \log a = \log b & Power Rule \\ \frac{y \log a}{\log a} = \frac{\log b}{\log a} & Isolate y \\ y = \frac{\log b}{\log a} \\ \log_{a} b = y = \frac{\log b}{\log a} ✓ \end{matrix}$

Note

Remember to start the problem by writing the first equation as an exponential equation.

Q: What is the variable you need to isolate?

A: y

Calculate the value of $\frac{\log b}{\log a}$ when $a = 5$ and $b = 19$ .

$\frac{\log 19}{\log 5} \approx 1.8295$

Say What You Know

In your own words, talk about what you have learned using the objectives for this lesson and your work on this page.

Note

Restate the objectives of the lesson in your own words. If you are unable to restate the lesson objectives, go back and reread the objectives and then explain them.

Approximate the value of logarithm expressions.
Solve logarithmic equations with common logs.