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\(\large b^x = b^y \Rightarrow x = y \) iff \(\large b > 0, b \neq 1\) Why b>0? Why not b ≠ 0?

Mathematics
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(-1)^3=(-1)^5 => 3=5. True or false?
Ok, how about b≠-1, 0, 1? I just don't understand why b couldn't be smaller than zero...
-1 is smaller than 0

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Other answers:

The statement did not work for b<0
except -1... Why couldn't it be smaller than zero?
except -1...
Why not \(b \in \mathbb{R}, b \neq -1, 0, 1\)?
Is the the thingy suppose to go both ways?
Or do you mean it just in that one way?
Well, both way, I guess.
I found this statement in a iPhone app called Math Formulas, I think this is wrong, but I'm not sure...
Well it is probably leading up to logarithms... Of course 1^n=1^m but this does not imply n=m.
Oh you understand why b cannot be -1,0, or 1.
Have you talked about logarithms?
\[\log_b(x)=\frac{\ln(x)}{\ln(b)} , x>0, b>0, b \neq 1\]
\[b^x=b^y\] \[\log_b(b^x)=\log_b(b^y)\] \[x \log_b(b)=y \log_b(b)\] \[x(1)=y(1)\] \[x=y\]
That is assuming b>0 and b does not equal 1.
Well, this makes sense. Thanks.

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