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

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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.

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