Thread: Whether it is possible to present the sum of two composed, as work of these composed?

Whether it is possible to present the sum of two composed, as work of these composed, erected in some degrees:$\displaystyle a+b = a^{f(x)}b^{g(y)}$
$\displaystyle f(x)=?$
$\displaystyle g(y)=?$

$\displaystyle a+b = a^{f(x)}b^{g(y)} $

$\displaystyle \ln (a+b) = \ln (a^{f(x)}b^{g(y)}) $

$\displaystyle \ln (a+b) = \ln(a^{f(x)} ) + \ln (b^{g(y)}) $

$\displaystyle \ln(a^{f(x)} ) = \ln (a+b) - \ln (b^{g(y)}) $

$\displaystyle f(x) = \frac{ \ln\left( \frac{a+b}{b^{g(y)}}\right))}{\ln (a) }$

same way u can find g(y)