# Prove by method of induction log a x^n = n loga x, x > 0, n ∈ N

41 views

closed

Prove by method of induction loga xn = n loga x, x > 0, n ∈ N

+1 vote
by (45.9k points)
selected

Let P(n) = loga xn = n loga x, x > 0, n ∈ N.

Step IV:

From all the steps above, by the principle of mathematical induction, P(n) is true for all n ∈ N.

$\therefore$ logaxn = n loga x, x > 0, n ∈ N.