Solving exponential equationsAQA A-Level Maths: Mind map

Exam questions on Solving exponential equations

1. The equation $5^x=40$ is to be solved using logarithms.
   Hence, or otherwise, solve $5^{x-1}=40$, giving your answer to 3 significant figures.2 marks
2. £2000 is invested in an account that pays 3.5% compound interest per year. After $n$ complete years the value of the investment is £$2000\times1.035^n$.
   Find the smallest whole number of years after which the investment is worth more than £5000.2 marks
3. Two equations are given: $4^{3x-1}=100$ and $3\mathrm{e}^{2x}=21$.
   Solve $4^{3x-1}=100$, giving your answer to 3 significant figures.3 marks