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1 Unit 1: Pure Mathematics A

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Question 221

Let x>0x>0x>0, a>0 a>0\,a>0 and a≠1a\ne1a=1. Let k k\,k be a real number for which xk x^k\,xk is defined.

Starting from the definition of a logarithm, prove that log⁡a(xk)=klog⁡ax\log_a(x^k)=k\log_a xloga​(xk)=kloga​x.

[4]
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1 Unit 1: Pure Mathematics A Questions

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