4^x + 3^x= 5^x
From Pythagorean triple principle,
the square of a number plus the square of another number should give a corresponding square of a new number.
So,
a^2 + b^2= c^2 is an illustration
Thus, relating the expression, 4^x + 3^x= 5^x to a^2 + b^2= c^2, x should automatically equals 2.
5 months ago
taking log of both sides
logx + logx = logx
4 3 5
making a change of base (all log carrier base 10)
logx + logx = logx
___ ___ ___
log4 log3 log5
log(x-4) + log(x-3) =log(x-5)
log(x-4+x-3) = log(x-4)
2x-7=x-5
2x-x=7-5
x=2