geerky42
  • geerky42
\(\large b^x = b^y \Rightarrow x = y \) iff \(\large b > 0, b \neq 1\) Why b>0? Why not b ≠ 0?
Mathematics
schrodinger
  • schrodinger
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freckles
  • freckles
(-1)^3=(-1)^5 => 3=5. True or false?
geerky42
  • geerky42
Ok, how about b≠-1, 0, 1? I just don't understand why b couldn't be smaller than zero...
freckles
  • freckles
-1 is smaller than 0

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freckles
  • freckles
The statement did not work for b<0
geerky42
  • geerky42
except -1... Why couldn't it be smaller than zero?
geerky42
  • geerky42
except -1...
geerky42
  • geerky42
Why not \(b \in \mathbb{R}, b \neq -1, 0, 1\)?
freckles
  • freckles
Is the the thingy suppose to go both ways?
freckles
  • freckles
Or do you mean it just in that one way?
geerky42
  • geerky42
Well, both way, I guess.
geerky42
  • geerky42
I found this statement in a iPhone app called Math Formulas, I think this is wrong, but I'm not sure...
freckles
  • freckles
Well it is probably leading up to logarithms... Of course 1^n=1^m but this does not imply n=m.
freckles
  • freckles
Oh you understand why b cannot be -1,0, or 1.
freckles
  • freckles
Have you talked about logarithms?
freckles
  • freckles
\[\log_b(x)=\frac{\ln(x)}{\ln(b)} , x>0, b>0, b \neq 1\]
freckles
  • freckles
\[b^x=b^y\] \[\log_b(b^x)=\log_b(b^y)\] \[x \log_b(b)=y \log_b(b)\] \[x(1)=y(1)\] \[x=y\]
freckles
  • freckles
That is assuming b>0 and b does not equal 1.
geerky42
  • geerky42
Well, this makes sense. Thanks.

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