Question

Solve the equation
Xp+yq=z

Answer 1

The solution of the given equation is $f(\frac{x}{y} ,\frac{y}{z}) = 0$.

Given : We are given the equation xp+yq = z.

To find: We need to find the solution to this equation.

Solution:

The subsidiary equations are,

$\frac{dx}{x} = \frac{dy}{y} =\frac{dz}{z}$

From the first two fractions, we get,

$\frac{dx}{x} = \frac{dy}{y}$

Solving them we get,

log x = log y + log a

or a = x/y

From the second and third fraction we get,

$\frac{dy}{y} =\frac{dz}{z}$

log y = log z + log b

or b = y/z

Hence, the solution of the given equation is

$f(\frac{x}{y} ,\frac{y}{z}) = 0$.

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