Logarithms and their lawsAQA A-Level Maths: Mind map

Exam questions on Logarithms and their laws

1. In this question, evaluate each logarithm without using a calculator.
   Find the exact value of $\log_48$.2 marks
2. Let $a=\log_{10}2$ and $b=\log_{10}3$.
   Write $\log_{10}\sqrt{18}$ in terms of $a$ and $b$.2 marks
3. The positive real numbers $x$ and $y$ are such that $\ln x=p$ and $\ln y=q$.
   Express $\ln\left(\dfrac{x^3}{\sqrt y}\right)$ in terms of $p$ and $q$.3 marks