If $3^x +3^y +3^z=9^{13}$.Find value of $x+y+z$ Problem: If $3^x +3^y +3^z=9^{13}$.Find value of $x+y+z$.
Solution:  $3^x +3^y +3^z=9^{13}$
$3^x +3^y +3^z=3^{26}$
I am unable to continue from here.
Any assistance is appreciated.
Edited
$9^{13} =3^{26}$
$=3^{25} (3)$
$=3^{25} (1+1+1)$
$=3^{25} + 3^{25} + 3^{25}$
So $x+y+z =75$

Let $x\ge y\ge z$. Then
$$3^x +3^y +3^z=3^{26}$$
$$3^z(3^{x-z}+3^{y-z}+1)=3^{z}\cdot3^{26-z}$$
$$3^{x-z}+3^{y-z}+1=3^{26-z} \Leftrightarrow x=z=y=25$$
