Exploring Exponential and Logarithmic Equations

1. Convert the following expressions between exponential and logarithmic form.

2. Solve for ????. Give your answer to three decimal places where appropriate.

3. Use the properties of logarithms to solve the following equations

4. Solve for the unknown using a method of your choice.

6. Write the equation of a logarithmic function that has been vertically stretched by 4, reflected in the x-axis, horizontally compressed by 1/9, moved 11 units up and 12 units left. Justify your answer.

7. Ethan bought a new car worth $54,000. After 5 years, the car was worth $28,497.52. Calculate the annual depreciation rate of Ethan’s car.

8. The hydrogen ion concentration of a lemon is about 0.02. What is its pH?

9. How do the intensities of a magnitude 6.0 earthquake and a magnitude 2.9 earthquake compare?

sketch or screenshot in your solution.

12. Why must the base of a logarithm be positive?

13. Why can we not calculate the logarithm of a negative number?

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