1.9 Laws of logarithmsIB Maths: Applications and Interpretation HL: Flashcards

What these 12 flashcards ask

\logax=y means what?
State the product law of logarithms.
State the quotient law of logarithms.
State the power law of logarithms.
What bases do exam questions use?
\ln e^{x} simplifies to?
Value of \loga1 and of \logaa?
Is \log(x+y)=\log x+\log y?
Solve 3^{x}=50.
Write \ln15 using \ln3 and \ln5.
What does a log scale do to a factor of 10?
How do you linearise y=kx^{n}?

Exam questions on 1.9 Laws of logarithms

Let $a=\ln3$ and $b=\ln5$ .
Express $\ln\sqrt{45}$ in terms of $a$ and $b$ .2 marks
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).