1.5 Laws of exponents and introduction to logarithmsIB Maths: Applications and Interpretation HL: Flashcards

What these 13 flashcards ask

Product law for exponents?
Quotient law for exponents?
Power of a power?
What is a^{-n}?
What is a^{0} for a\neq0?
Write (2x)^{-3} without a negative exponent.
Write (2x)^{4} expanded.
a^{x}=b in logarithm form?
What condition must b satisfy for \log{a}b to exist?
What does \ln x mean?
Value of \log{10}0.001?
Value of \ln e^{5}?
How do you evaluate \log{10}250?

Exam questions on 1.5 Laws of exponents and introduction to logarithms

In this question, $x\neq0$ .
Write $\frac{(2x^{3})^{4}}{8x^{5}}$ in the form $kx^{n}$ , where $k$ and $n$ are integers.2 marks
Logarithms with base $10$ and base $e$ are the inverse functions of $10^{x}$ and $e^{x}$ .
Use your GDC to write down the value of $\log_{10}250$ and the value of $\ln250$ , each correct to 3 significant figures.2 marks
A radioactive substance decays so that its mass, $m$ grams, after $t$ years is modelled by $m=80e^{-0.05t}$ .
Write down the initial mass, and use your GDC to find the mass after 10 years.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).