# Exam-Style Question on Logarithms

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 440. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

In an old science fiction book the author described the intensity of reverse polarity, $$P$$ measured in treckons, is a function of the nebula thrust, $$N$$ measures in whovians. The intensity level is given by the following formula.

$$P = 7 \log_{10}(N \times 10^{8}), N \ge 0$$

(a) An space shuttle has a nebula thrust of $$9.1 × 10^{-3}$$ whovians. Calculate the intensity level, $$P$$ of the shuttle.

(b) A different space shuttle has an intensity level of 112 trekons. Find its nebula thrust, $$N$$.

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