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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
3.20 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 93 = __________.
3 log 9
9 log 3

Q 2: log 72 = __________.
7 log 2
2 log 7

Q 3: log 52 = __________.
2 log 5
5 log 2

Q 4: log 62 = __________.
2 log 6
6 log 2

Q 5: log 83 = __________.
3 log 8
8 log 3

Q 6: log 82 = __________.
8 log 2
2 log 8

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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