geerky42
\(\large b^x = b^y \Rightarrow x = y \) iff \(\large b > 0, b \neq 1\)
Why b>0? Why not b ≠ 0?



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freckles
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(1)^3=(1)^5 => 3=5.
True or false?

geerky42
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Ok, how about b≠1, 0, 1?
I just don't understand why b couldn't be smaller than zero...

freckles
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1 is smaller than 0

freckles
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The statement did not work for b<0

geerky42
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except 1... Why couldn't it be smaller than zero?

geerky42
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except 1...

geerky42
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Why not \(b \in \mathbb{R}, b \neq 1, 0, 1\)?

freckles
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Is the the thingy suppose to go both ways?

freckles
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Or do you mean it just in that one way?

geerky42
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Well, both way, I guess.

geerky42
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I found this statement in a iPhone app called Math Formulas, I think this is wrong, but I'm not sure...

freckles
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Well it is probably leading up to logarithms...
Of course 1^n=1^m but this does not imply n=m.

freckles
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Oh you understand why b cannot be 1,0, or 1.

freckles
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Have you talked about logarithms?

freckles
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\[\log_b(x)=\frac{\ln(x)}{\ln(b)} , x>0, b>0, b \neq 1\]

freckles
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\[b^x=b^y\]
\[\log_b(b^x)=\log_b(b^y)\]
\[x \log_b(b)=y \log_b(b)\]
\[x(1)=y(1)\]
\[x=y\]

freckles
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That is assuming b>0 and b does not equal 1.

geerky42
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Well, this makes sense. Thanks.