1Expand log₄(3x) and state the Law that is indicated.

2 Expand log₃(27/x) and state the Law that is indicated.

3 Expand log₄ x⁵ and state the Law that is indicated.

4 Expand log₄(4/7x²) and state the Law that is indicated.

B Simplify and indicate which law is applied. Show steps as done in the examples. (See Exs. 5 and 6)

5 log₄ 24 - log₄ 6

6 log₃ 10 + 3 log₃ 2

7 3 log 3 - log 9

C Letlog_b 3 = 0.5646,log_b 4 = 0.7124, andlog_b 5 = 0.8271. UsIng these values and showing steps, evaluate the following. (See Ex. 10)

8. log_b 15 -log_b (4/3)

D 9 Use the change of base formula to find the value of log₄ 15 to three significant figures.Show steps as done in Example 11

E Apply Your Knowledge

10 Voltage, like pressure, appears squared in expressions for power or intensity. So, by convention, we define:

gain = 20 log (V_out/V_in)

An amplifier has an input of 10 mV and an output of 3 V. What is its voltage gain in dB?Show steps as done in Ex.12.