T = kr^(−5/p) express p in terms of k, r and T

asked by guest
on Oct 24, 2024 at 8:31 pm



You asked:

Given \(T = k \cdot {r}^{\frac{-5}{p}}\), express \(p\) in terms of the variables \(k\), \(r\) and \(T\).

MathBot Answer:

$$\begin{aligned}p &= \frac{5 \log{\left(r \right)}}{\log{\left(\frac{k}{T} \right)}}\\p &= \frac{\log{\left(r \right)}}{\log{\left(\frac{\sqrt[5]{\frac{k}{T}} \left(-1 + \sqrt{5} - \sqrt{2} \sqrt{-5 - \sqrt{5}}\right)}{4} \right)}}\\p &= \frac{\log{\left(r \right)}}{\log{\left(\frac{\sqrt[5]{\frac{k}{T}} \left(-1 + \sqrt{5} + \sqrt{2} \sqrt{-5 - \sqrt{5}}\right)}{4} \right)}}\\p &= \frac{\log{\left(r \right)}}{\log{\left(\frac{\sqrt[5]{\frac{k}{T}} \left(- \sqrt{5} - 1 - \sqrt{2} \sqrt{-5 + \sqrt{5}}\right)}{4} \right)}}\\p &= \frac{\log{\left(r \right)}}{\log{\left(\frac{\sqrt[5]{\frac{k}{T}} \left(- \sqrt{5} - 1 + \sqrt{2} \sqrt{-5 + \sqrt{5}}\right)}{4} \right)}}\end{aligned}$$

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