A. Solve the following showing all steps as done in the examples in the lesson content.

1.log₂(x) =log₂(18)

2.log_bx²=log_b(4x - 4)

3.log_b(x²- 56)=log_b(x)

4.2log_b(x) =log_b(2x-2) +log_b(2)

5. ln(e^x) = ln(e⁹) - ln(e⁶)

6.log₂(32) = x

7.log₂(x - 4) +log₂(x) = 5

8.log₂(log₂(x)) = 2

9. ln(x) = 4

10.log₂(x) = 3.87

11.log₂(2x) = 5.23

12. ln(3.1x) = 2.31

B. Solve the following problems showing your steps and including the units of measurement.

13. The population P of a city increases according to the formula

P = 5000 e^{a t}

where t is in years and t = 0 corresponds to 1980. In 1990, the population was 10000. Find the value of the constant a and approximate your answer to 3 decimal places.

14. "Loudness" is measured in decibels. The formula for the loudness of a sound is given by "Db = 10log[ I / I₀]" where I₀is the intensity of "threshold sound", or sound that can barely be perceived. How many decibels is a noise with an intensity of I = (9 * 1010)^I₀?