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

**d425473** · March 29th 2012, 01:00 AM

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

**Amer** · March 30th 2012, 09:21 AM

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

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

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

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

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

same way u can find g(y)

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

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