|log x am = m log x a.|
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.
Directions: Solve the following problems. Also write at least ten examples of your own.