Explore
In Try This 1 you were solving logarithmic equations. A logarithmic equation is an equation in which there is a logarithm of a variable. You may have found that when a logarithmic equation is in the form logc L = logc R, where the left side and right side each contain a single logarithm with the same base, the logarithms can be removed.
- If logc L = logc R, where c, L, R > 0 and c ≠ 1, then L = R.
Read “Link the Ideas” on page 406 of the textbook. Notice that a proof of the preceding property is provided.
In Try This 2 you will use this property: if logc L = logc R, then L = R. You will explore how to solve a more difficult logarithmic equation.
Try This 2
Use the logarithmic equation log2 (x − 2) + log2 (x + 1) = 2 for the following questions.
- Using a law of logarithms, write the left side of the equation as a single logarithm.
- Use your answer from question 1 and write the equation with the single logarithm on the left side and “equal to 2” on the right side. Change the equation to exponential form and solve for x.
- Write the right side of the equation as a single logarithm. This logarithm should have the same base as the logarithm on the left side and the logarithm should equal 2.
- Use your answers from questions 1 and 3 to solve the equation for x.
- How could you check to see if your answers are correct?
- Are all of your solutions correct? Explain your answer.
- Explain why the logarithm of a negative number is undefined.
Save your responses in your course folder.
