IB Maths AA HL Sl 1 5 Integer Exponents and Logarithms Questions

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

Exam points

Apply laws of integer exponents and logarithms to simplify and solve equations.
Calculate unknown exponents or logarithms and interpret results using complete mark-scheme evidence.

[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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IB Maths AA HL Sl 1 5 Integer Exponents and Logarithms Questions question 1