Question

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

Answer 1

Let P(n) = log_a xⁿ = n log_a 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.

\(\therefore\) log_axⁿ = n log_a x, x > 0, n ∈ N.