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### High School Mathematics3.20 Logarithm of a Power

 log x am = m log x a. Proof: Let log x am = p then xp = am----------I log x a = q then a = xq ---------II From I and II, am = (xq)m = xqm; [Since (xm)n = xmn]------III From I and III, we get am = ap = xqm Therefore, p = qm Therefore, log x am = m log x a The logarithm of any power of a number is equal to the product of the logarithm of the number and the index of the power. Example: log 10 23 = 3 log 10 2 Directions: Solve the following problems. Also write at least ten examples of your own.
 Q 1: log 62 = __________.6 log 22 log 6 Q 2: log 52 = __________.5 log 22 log 5 Q 3: log 37 = __________.3 log 77 log 3 Q 4: log 82 = __________.2 log 88 log 2 Q 5: log 152 = __________.15 log 22 log 15 Q 6: log 72 = __________.7 log 22 log 7 Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!