1.9 Laws of logarithmsIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 1.9 Laws of logarithms

1. Let $a=\ln3$ and $b=\ln5$.
   Express $\ln\sqrt{45}$ in terms of $a$ and $b$.2 marks
2. The sound level $L$ decibels (dB) of a noise of intensity $I$ W m$^{-2}$ is given by $L=10\log_{10}\left(\frac{I}{10^{-12}}\right)$.
   Use your GDC to find the intensity of a noise with sound level $85$ dB.2 marks
3. A culture of bacteria grows so that after $t$ hours there are $N=800e^{0.35t}$ bacteria.
   Find the time taken for the population to double. Give your answer in hours to 3 significant figures.3 marks