<s>[INST] what are the zeroes of $f(x) = 2^x + 3^x - 5^x?$ 1) How do I find the number of zeroes of such exponential equations? 
2) Is there any easier way to manually plot such sum of exponential functions?
 [/INST] At $x=0$, we know that the formula becomes $3^0+2^0-5^0=1+1-1=1$, and when $x<0$ $3^x>5^x$ and $2^x>5^x$. Therefore, $2^x+3^x>5^x$, and there are no roots for $x<0$. For $x>0$, we know that $2^x<3^x<5^x$, so at some point $5^x=2^x+3^x$ and at point $x$ there will be a zero. That just happens to be $x=1$ since $2^x+3^x-5^x=2^1+3^1-5^1=2+3-5=5-5=0$. 
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