IB Maths AA HL 1.7 Rational exponents, logarithm laws and proof Question Bank

Practise IB Maths AA HL 1.7 by combining exponent rules, logarithm laws and exact reasoning in multi-step problems.

Exam points

Derive or verify a logarithmic identity while preserving base, argument and domain conditions.
Solve a parameterised exponential or logarithmic equation and reject extraneous solutions.
Connect exact exponent or logarithm manipulation to an applied decay, growth or temperature model.

[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

SL 1.7—Rational exponents and logarithm laws question 1