# Equations and word problems involving logarithms

1. Solve for x in the following equations.

a. log-base-3(x - 5) + log-base-3(x + 3) = 2

b. log-base-7(x) + log-base-7(x - 1) = log-base-7(2x)

2. Show that the following statement is true. Please refer to the attachment for the statement.

3. A quantity of oxygen gas had 16.32g of the radioactive isotope oxygen-19 in it. When measured exactly 10 minutes later, the amount of oxygen-19 was 0.964g. What is the half-life, in seconds, of oxygen-19?

4. Give an example of a logarithmic equation that can not be solved and explain why it can not be solved.

5. Is log-base-3(5) equal to log-base-5(3)? Explain your answer. Do not evaluate the logarithms.

6. State the product law for logarithms. Is it possible to use the product law for logarithms to evaluate the expression log(-7) + log(-4)? Explain your answer.

7. Describe the steps you would say over the telephone to explain how to solve the equation log-base-3(x) + log-base-3(x + 2) = 1 .

8. Jacob had told Anderson to take ear protection when he went to his rock concert. Anderson said he looked up sound levels at concerts on the Internet. He saw that a conversation was rated at 60 dB and a rock concert at 120 dB. He explained to Jacob that the concert was only twice as loud as the conversation they were having. What did Jacob say in response to Anderson's claim?

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#### Solution Summary

Several equations and word problems involving logarithms of different bases are solved. The solutions are in a DOC file.