Solving logarithmic equations

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(x) = 8

7. log₂(32) = x

8. log₂(x - 4) + log₂(x) = 5

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. Earthquake intensity is measured by the Richter scale. The formula for the Richter rating of a given quake is given by "R=log[I/I₀]" where I₀is the "threshold quake", or movement that can barely be detected, and the intensity I is given in terms of multiples of the threshold intensity.

An earthquake was reported to have a Richter number of 5.99. How does the intensity of the earthquake approximately compare with the reference intensity?

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?