Logarithms and their lawsEdexcel A-Level Maths: Mind map

Exam questions on Logarithms and their laws

1. Consider the logarithms $\log_5125$ and $\log_2\frac18$.
   Find the value of $\log_48$.2 marks
2. Let $p=\log_a2$ and $q=\log_a5$, where $a>1$.
   Express $\log_a\sqrt{20}$ in terms of $p$ and $q$.2 marks
3. The value $\pounds V$ of one savings account after $t$ years is $V=2000e^{0.04t}$. A second account has value $\pounds W=1500\times1.05^t$ after $t$ years.
   Find how many years it takes for the first account to reach $\pounds3000$, giving your answer to 3 significant figures.3 marks