Mastery Check Solutions

Show What You Know

Evaluate the logarithmic expressions.

$\log_{125} 5$

$\begin{array}{rcl} \log_{125} 5 & = & x \\ 125^{x} & = & 5 \\ 5^{3 (x)} & = & 5^{1} \\ 3 x & = & 1 \\ x & = & \frac{1}{3} \end{array}$

$\log_{125} \frac{1}{5}$

$\begin{array}{rcl} \log_{125} \frac{1}{5} & = & x \\ 125^{x} & = & \frac{1}{5} \\ 5^{3 (x)} & = & 5^{- 1} \\ 3 x & = & - 1 \\ x & = & - \frac{1}{3} \end{array}$

$\log_{5} 125$

$\begin{array}{rcl} \log_{5} 125 & = & x \\ 5^{x} & = & 125 \\ 5^{x} & = & 5^{3} \\ x & = & 3 \end{array}$

$\log_{5} \frac{1}{125}$

$\begin{array}{rcl} \log_{5} \frac{1}{125} & = & x \\ 5^{x} & = & \frac{1}{125} \\ 5^{x} & = & 5^{- 3} \\ x & = & - 3 \end{array}$

Note

The expressions are intentionally similar. Work carefully.

Q: Why do you need to set the expression equal to x?

A: To be able to determine the value of the log

Draw a line matching the exponential expression to its correct logarithmic expression.

Note

This is a self-checking activity to confirm your answers in part A.

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.

Write an exponential expression or equation in logarithmic form. 
Write a logarithmic expression or equation in exponential form. 
Evaluate a logarithmic expression.