For instance, I know that in $4^x + 5^x = 41$ ; $x = 2$
I tried doing $x[\log(4) + \log(5)] = \log(41)$, but that's not right.
Is there anyway to solve this using logs. I think there's a way to solve it by graphing but I wanted to see if I can do it on paper alone.
Thank you!
No, you can not.
By the way, $f(x)=4^x+5^x$ increases and we get an unique root: $2$.