Exponential logic

Algebra Level 2

What about the correctability of this statement?

x a = y b ⇔ a = b \large{ { x }^{ a }={ y }^{ b }\Leftrightarrow a=b}

Note: x x , y y , a a and b b can be the same or different.

Always FALSE Always TRUE Not always TRUE but not always FALSE

Evan Huynh by Evan Huynh , 24, Sweden

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1 solution

Evan Huynh
Dec 20, 2015

The statement is TRUE except in the following cases:

x = y = 0: a and b can be any number.

Example: 0 2 = 0 3 0^{2} = 0^{3}

x = 1 or y = 1

Example: 1 2 = 1 3 1^{2} = 1^{3} and 3 0 = 1 3 3^{0} = 1^{3}

x = -1 or y = -1

Example: ( − 1 ) 2 = ( − 1 ) 4 (-1)^{2} = (-1)^{4} and 3 0 = ( − 1 ) 2 3^{0} = (-1)^{2}

Therefore, it's not always TRUE but not always FALSE.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

It is not clear to me what you are trying to express here.

The statement is true if x = y ≠ 1 , 0 x = y \neq 1, 0 .

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