1 Unit 1: Pure Mathematics A

Let $u > 0$ , $v > 0$ , $a>0\,$ and $a≠1a\ne1$ .

Starting from the definition of a logarithm, prove that $log⁡a(u2v3)=2log⁡au−3log⁡av\log_a\left(\dfrac{u^2}{v^3}\right)=2\log_a u-3\log_a v$ .

Your proof must not quote any logarithm law.

[6]

Let $u > 0$ , $v > 0$ , $a>0\,$ and $a≠1a\ne1$ .

Starting from the definition of a logarithm, prove that $log⁡a(u2v3)=2log⁡au−3log⁡av\log_a\left(\dfrac{u^2}{v^3}\right)=2\log_a u-3\log_a v$ .

Your proof must not quote any logarithm law.

[6]

1 Unit 1: Pure Mathematics A Questions