<s>[INST] 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 $x+y+z =75$
 [/INST] If $x=y=z$ then clearly $x=y=z=25$ works.
Otherwise, this is a ternary number with sum of digits $3$. But the unique representation of this number in ternary is 
$$1\underbrace{0 \ldots 0}_{26 \text{ times}}$$ 
which has a sum of digits as $1$.
</s>