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If x, a and b are a real numbers and x^a = x^b, does this implies a = b??

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Kirill Z. | Physics, math tutor with great knowledge and teaching skillsPhysics, math tutor with great knowledge...
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x=1, a=6, b=7;
16=1; 17=1; So, x=1, a≠b, but xa=xb. That is, xa=xb does not necessarily implies a=b.
Andre K. | High school and college math, programming, statistics, SAT/ACT, etc.High school and college math, programmin...
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Hi Harry,
What if x=0? Must a and b be equal then?