IB Maths AA HL 1.5 Integer exponents and logarithms Question Bank

Practise IB Maths AA HL 1.5 through questions that extend logarithms to parameters, exponential models and multi-step restrictions.

Exam points

Transform HL exponential and logarithmic equations while tracking parameters, domains and base restrictions.
Use logarithms to solve model thresholds and justify which mathematical solution remains valid in context.
Compare exact and approximate forms and explain the contextual meaning of the selected logarithmic result.

[Maximum number: 2]

It is given that $\log _{10} a=\frac{1}{3}$ , where a>0.
Find the value of

$\quad \log _{10}\left(\frac{1}{a}\right)$ ;

$\log _{10} 1-\log _{10} a$ OR $\log _{10} a^{-1}=-\log _{10} a$ OR $\log _{10} 10^{-\frac{1}{3}}$ OR $10^{x}=\frac{1}{10^{\frac{1}{3}}}$ $=-\frac{1}{3}$

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SL 1.5—Integer exponents and logarithms question 1