# Solve (sic) for z: y^z/x^4 = y^3/x^z ?

Jan 5, 2017

$z = \frac{4 \ln x + 3 \ln y}{\ln x + \ln y}$

#### Explanation:

Clearly you can't "solve" for $z$ here but you can express $z$ in terms of $x$ and $y$ as follows:

${y}^{z} / {x}^{4} = {y}^{3} / {x}^{z}$

Cross multiply $\to {x}^{z} \cdot {y}^{z} = {x}^{4} \cdot {y}^{3}$

Take logs of both sides $\to z \ln x + z \ln y = 4 \ln x + 3 \ln y$

$z \left(\ln x + \ln y\right) = 4 \ln x + 3 \ln y$

$z = \frac{4 \ln x + 3 \ln y}{\ln x + \ln y}$

Hope this was what you were looking for.