Laws of logarithmsEdexcel International A Level Maths: Mind map

Exam questions on Laws of logarithms

1. Given that $\log_a 2=p$ and $\log_a 5=q$, where $a$ is a positive constant and $a\neq1$.
   Express $\log_a\left(\frac{25}{8}\right)$ in terms of $p$ and $q$.2 marks
2. $x$ and $y$ are positive real numbers and $a$ is a positive constant with $a\neq1$. $\log_a x=3$ and $\log_a y=5$.
   Find the value of $\log_a\left(\frac1{x^2y}\right)$.2 marks
3. Throughout this question $a$ is a positive constant with $a\neq1$. Do not use a calculator.
   Show that $\log_a48-\log_a3=4\log_a2$.3 marks