## Exam-Style Question on Logarithms## A mathematics exam-style question with a worked solution that can be revealed gradually |

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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