1.5 Laws of exponents and introduction to logarithmsIB Maths: Applications and Interpretation SL: Mind map

Exam questions on 1.5 Laws of exponents and introduction to logarithms

1. 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
2. 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
3. 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