Solving $x = \left(\frac{ab}{cd}\right)^{0.68}$ for $a$.

Question

My equation is $$x = \left(\frac{ab}{cd}\right)^{0.68}.$$

How do I find $a$? I am out of ideas here.

Thanks.

Answer 1

Hint:

For $x\ge 0$: $$ \left(\frac{ab}{cd}\right)^{\frac{68}{100}}=x\quad \Rightarrow \quad \frac{ab}{cd}=x^{\frac{100}{68}} $$

now find $a$

Answer 2

We have $\log(x)=0.68\log\left(\frac{ab}{cd}\right)=0.68(\log(a)+\log(b)-\log(cd))$ implies that $$\begin{align}a&=e^{\frac{100}{68}\log(x)+\log(cd)-\log(b)}\\ &=\frac{x^{\frac{100}{68}}cd}{b}. \end{align}$$

This is assuming $b\neq 0$.