IB Maths AI SL 1.5 Integer Exponents and Logarithms Questions

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, rearrange or compare expressions, including equivalent base-10 and natural-log forms.
Solve exponential and logarithmic equations, selecting valid bases, domains and parameter values.
Use logarithmic scales or inverse exponentials in contextual calculations such as pH, sound, brightness, information or decay.
Interpret the numerical solution, checking domain, units, scale and whether the model’s condition is satisfied.

[Maximum number: 4]

"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 ]

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

(c)

Explain what these coordinate values mean in the context of computer passwords.

[ 1 ]

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IB Maths AI SL 1.5 Integer Exponents and Logarithms Questions question 1

Question (a)

Question (b)

Question (c)