IB Maths AA HL Sl 1 7 Rational Exponents and Logarithm Laws Questions

Practise manipulating exponentials and logarithms exactly, preserving base and domain conditions, solving parameterised equations and interpreting growth or decay models.

Exam points

Apply laws of rational exponents and logarithms to simplify expressions and solve equations.
Use change-of-base and logarithm identities accurately with complete mark-scheme evidence.

[Maximum number: 3]

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

$\log _{1000} a$ .

$\frac{\log _{10} a}{\log _{10} 1000}$ OR $\frac{1}{3} \log _{1000} 10$ OR $\log _{1000} \sqrt[3]{1000^{\frac{1}{3}}}$ OR $10^{\frac{1}{3}}=1000^{x}\left(=\left(10^{3}\right)^{x}\right)$ $\frac{\log _{10} a}{3}$ OR $\frac{1}{3} \log _{1000} 1000^{\frac{1}{3}}$ OR $\log _{1000} 1000^{\frac{1}{9}}$ OR $3 x=\frac{1}{3}$ $=\frac{1}{9}$

All question bank results loaded

IB Maths AA HL Sl 1 7 Rational Exponents and Logarithm Laws Questions question 1