Solve (sic) for $z$ $z$ : $\frac{y^{z}}{x^{4}} = \frac{y^{3}}{x^{z}}$ $y^z/x^4 = y^3/x^z$ ?

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Answer 1 · 2017-01-05T05:19:30

$z = \frac{4 ln x + 3 ln y}{ln x + ln y}$ $z=(4lnx+3lny)/(lnx+lny)$

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

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

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

Take logs of both sides $\to z ln x + z ln y = 4 ln x + 3 ln y$ $-> zlnx+zlny = 4lnx+3lny$

$z (ln x + ln y) = 4 ln x + 3 ln y$ $z(lnx+lny)= 4lnx+3lny$

$z = \frac{4 ln x + 3 ln y}{ln x + ln y}$ $z=(4lnx+3lny)/(lnx+lny)$

Hope this was what you were looking for.

Solve (sic) for zz: yzx4=y3xzy^z/x^4 = y^3/x^z ?