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1 Unit 1: Pure Mathematics A

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Question 150

Let x>0x>0x>0, y>0y>0y>0, a>0 a>0\,a>0 and a≠1a\ne1a=1.

Starting from the definition of a logarithm, prove that log⁡a(xy)=log⁡ax−log⁡ay\log_a\left(\dfrac{x}{y}\right)=\log_a x-\log_a yloga​(yx​)=loga​x−loga​y.

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1 Unit 1: Pure Mathematics A Questions

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