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1 Unit 1: Pure Mathematics A

Let $m\,$ and $n\,$ be real numbers, and let $a>0\,$ with $a≠1a\ne1$ .

Given that $x=a^m$ and $y=a^n$ , prove that $log⁡a(x2y3x)=32m+3n\log_a\left(\dfrac{x^2y^3}{\sqrt{x}}\right)=\dfrac32m+3n$ .

[5]

1 Unit 1: Pure Mathematics A Questions

Let $m\,$ and $n\,$ be real numbers, and let $a>0\,$ with $a≠1a\ne1$ .

Given that $x=a^m$ and $y=a^n$ , prove that $log⁡a(x2y3x)=32m+3n\log_a\left(\dfrac{x^2y^3}{\sqrt{x}}\right)=\dfrac32m+3n$ .

[5]