Prove that if a > 0, a 1, then alogax = x for all x

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Prove that if a > 0, a ≠ 1, then alogax = x for all x ∈ (0, ∞) and loga(ay) = y for all y ∈ R. Therefore the function x → logax on (0, →) to R is inverse to the function y → ay on R.
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Introduction to Real Analysis

ISBN: 978-0471433316

4th edition

Authors: Robert G. Bartle, Donald R. Sherbert

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