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How do I solve for an unknown in the base of an exponential equation. In my example W is unknown: $$PPV=K\cdot\left(\frac{D}{W^{0.5}}\right)^{-1.6}$$

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  • $\begingroup$ Start with dividing both sides by $K$ and then raise both sides to the power $\dfrac{-1}{1.6}$ $\endgroup$ – David Peterson Aug 30 '16 at 6:00
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I will do the first step.

$$PPV=K\cdot\left(\frac{D}{W^{0.5}}\right)^{-1.6} \implies \left(\frac{PPV}{K}\right)^{-5/8}\cdot \frac{1}{D}=\frac{1}{W^{.5}}.$$

Can you see how very mild manipulation will yield the answer? The idea here is to see how to express one variable ($W$) in terms of the rest.

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