IB Maths AI SL 1.5 Integer exponents and logarithms Question Bank

Practise IB Maths AI SL 1.5 through questions on integer powers, logarithm laws, changing bases and equations from applied contexts.

Exam points

Apply laws of integer exponents and logarithms to simplify expressions and expose the unknown.
Solve SL exponential or logarithmic equations and interpret the solution in context.
Check domain restrictions, base conditions and numerical accuracy before reporting the answer.

[Maximum number: 3]

"Password entropy" is a measure of the predictability of a computer password. The higher the entropy, the more difficult it is to guess the password.
The relationship between the password entropy, p, (measured in bits) and the number of guesses, G, required to decode the password is given by $0.301 p=\log _{10} G$ .

(a)

Calculate the value of p for a password that takes 5000 guesses to decode.

[ 2 ]

attempt to substitute 5000 for G
$0.301 p=\log _{10} 5000$
( p= ) 12.3 (bits) ( $12.2889 \ldots$ )

(b)

Write down G as a function of p.

[ 1 ]

$(G=) 10^{0.301 p} \quad \mathbf{OR} \quad 2^{p}$

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SL 1.5—Integer exponents and logarithms question 1

Question (a)

Question (b)