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anonymous

  • one year ago

log{b} 1000=3 I know b=10 but I don't understand how they got there.

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  1. anonymous
    • one year ago
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    \[\log_{b} 1000=3\]

  2. anonymous
    • one year ago
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    \[b^3=1000\] \[3\sqrt{b^3}= 3\sqrt{1000}\] b=10

  3. Nnesha
    • one year ago
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    well did you take 3rd root right ? you can write 1000 in terms of 3 exponents

  4. Nnesha
    • one year ago
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    x^3 =1000 ? what is x

  5. anonymous
    • one year ago
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    10

  6. anonymous
    • one year ago
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    What is the point of the 3's in front of the square root signs?

  7. Nnesha
    • one year ago
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    that's not 3 it's a 3rd rooot i guess like this \[\huge\rm \sqrt[3]{b^3}\]

  8. anonymous
    • one year ago
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    Right, I didn't know how to do that

  9. Nnesha
    • one year ago
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    you can convert 3rd to 1/3 exponent \[\huge\rm \sqrt[3]{b^3} = b^{3 \times \frac{ 1 }{ 3 }}\] so cancel out 3 exponent u have to take 3rd root :=)

  10. Nnesha
    • one year ago
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    \[\huge\rm \sqrt[3]{b^3} = b^{\cancel3 \times \frac{ 1 }{\cancel 3 }}=b\]

  11. anonymous
    • one year ago
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    Wouldn't that also mean that 1000 would be multiplied by 1/3?

  12. Nnesha
    • one year ago
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    yes so 1000 can be written as 10 to the 3rd power \[\huge\rm \sqrt[3]{10^3}\]

  13. anonymous
    • one year ago
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    See that's where I get confused, so the 1000 get simplified down to 10 because?

  14. Nnesha
    • one year ago
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    because it's easy to solve without calculator and it's legal :3

  15. anonymous
    • one year ago
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    -_- so because 10^3=1000 it gets simplified to 10^3 and since it's the 3rd root the exponent cancels out leaving b=10 ?

  16. Nnesha
    • one year ago
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    b to the 3rd power so you can either write 10 to the 3rd power or put 3rd root of 1000 into the calculator :=)

  17. Nnesha
    • one year ago
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    yep

  18. anonymous
    • one year ago
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    See when I enter that into my calc I get 94.86....

  19. Nnesha
    • one year ago
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    and it's helpful when you have to find an exponent given base for example 10^x = 1000

  20. Nnesha
    • one year ago
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    what did you enter ?

  21. freckles
    • one year ago
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    \[3 \sqrt{1000} \neq \sqrt[3]{1000}\]

  22. anonymous
    • one year ago
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    \[3\sqrt{1000}\]

  23. anonymous
    • one year ago
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    Yea see I don't know how to enter the latter

  24. Nnesha
    • one year ago
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    it's not 3 times square root of {1000} 3rd root like \[\sqrt[3]{1000}\]

  25. Nnesha
    • one year ago
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    ohh then convert 3rd root to 1/3 exponent \[\huge\rm \sqrt[3]{1000} = (1000)^\frac{ 1 }{ 3 }\]

  26. anonymous
    • one year ago
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    That works. =] Could you possibly help me with another problem?

  27. Nnesha
    • one year ago
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    gtg :3 sorry

  28. anonymous
    • one year ago
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    All's well Thank you for your help :)

  29. Nnesha
    • one year ago
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    my pleasure

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