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geerky42

  • 3 years ago

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

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  1. freckles
    • 3 years ago
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    (-1)^3=(-1)^5 => 3=5. True or false?

  2. geerky42
    • 3 years ago
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    Ok, how about b≠-1, 0, 1? I just don't understand why b couldn't be smaller than zero...

  3. freckles
    • 3 years ago
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    -1 is smaller than 0

  4. freckles
    • 3 years ago
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    The statement did not work for b<0

  5. geerky42
    • 3 years ago
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    except -1... Why couldn't it be smaller than zero?

  6. geerky42
    • 3 years ago
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    except -1...

  7. geerky42
    • 3 years ago
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    Why not \(b \in \mathbb{R}, b \neq -1, 0, 1\)?

  8. freckles
    • 3 years ago
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    Is the the thingy suppose to go both ways?

  9. freckles
    • 3 years ago
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    Or do you mean it just in that one way?

  10. geerky42
    • 3 years ago
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    Well, both way, I guess.

  11. geerky42
    • 3 years ago
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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...

  12. freckles
    • 3 years ago
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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.

  13. freckles
    • 3 years ago
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    Oh you understand why b cannot be -1,0, or 1.

  14. freckles
    • 3 years ago
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    Have you talked about logarithms?

  15. freckles
    • 3 years ago
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    \[\log_b(x)=\frac{\ln(x)}{\ln(b)} , x>0, b>0, b \neq 1\]

  16. freckles
    • 3 years ago
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    \[b^x=b^y\] \[\log_b(b^x)=\log_b(b^y)\] \[x \log_b(b)=y \log_b(b)\] \[x(1)=y(1)\] \[x=y\]

  17. freckles
    • 3 years ago
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    That is assuming b>0 and b does not equal 1.

  18. geerky42
    • 3 years ago
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    Well, this makes sense. Thanks.

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