IB Maths AA SL 1.5 Integer exponents & logarithms

IB Mathematics: analysis and approaches guide, first assessment 2021

Practise rewriting powers, logarithms and number bases, including exact log values, prime factors, radicals and base arithmetic.

How this is tested

rewrite logs such as log10(1/a) using index laws and log laws to obtain exact values
convert between bases or use digit divisibility conditions to determine unknown digits in a base number
simplify powers and radicals, including expressions such as (1-sqrt(3))^2 and integer remainders

[Maximum number: 1]

The loudness of a sound, L, measured in decibels, is related to its intensity, I units, by $L=10 \log _{10}\left(I \times 10^{12}\right)$ .
Consider two sounds, $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ .
$\mathrm{S}_{1}$ has an intensity of $10^{-6}$ units and a loudness of 60 decibels.
$\mathrm{S}_{2}$ has an intensity that is twice that of $\mathrm{S}_{1}$ .

State the intensity of $\mathrm{S}_{2}$ .

How this is tested

Question 4(a)