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geerky42 Group Title

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

  • 2 years ago
  • 2 years ago

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

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

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

    • 2 years ago
  4. freckles Group Title
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    The statement did not work for b<0

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

    • 2 years ago
  6. geerky42 Group Title
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    except -1...

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

    • 2 years ago
  8. freckles Group Title
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    Is the the thingy suppose to go both ways?

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

    • 2 years ago
  10. geerky42 Group Title
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    Well, both way, I guess.

    • 2 years ago
  11. geerky42 Group Title
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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...

    • 2 years ago
  12. freckles Group Title
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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.

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

    • 2 years ago
  14. freckles Group Title
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    Have you talked about logarithms?

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

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

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

    • 2 years ago
  18. geerky42 Group Title
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    Well, this makes sense. Thanks.

    • 2 years ago
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