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

Question id: 344. This question is similar to one that appeared on an IB Standard paper in 2017. The use of a calculator is allowed.

Consider the function \(f (x) = \log_p(24x - 18x^2)\) , for \(0 \lt x \lt 1\), where \(p \gt 0\).

The equation \(f (x) = 3\) has exactly one solution. Find the value of \(p\).

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