By " same base, same exponent " rule I mean :
$$b^x = b^n \iff x=n$$
Can the equation: $$ 2^x+4^x = 6$$ be solved by saying $$ 2^x+4^x = 6 = 2+4= 2^1 + 4^1$$ and consequently, that $$x = 1? $$
from Hot Weekly Questions - Mathematics Stack Exchange
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