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Denebel

How does this simplification work? Can someone show me the intermediate steps?

  • one year ago
  • one year ago

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  1. Denebel
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    |dw:1346313632906:dw|

    • one year ago
  2. juantweaver
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    \[\ln(x)*(\frac{1}{x*\ln10})+\log(x)*(1/x)=\frac{2*\ln(x)}{x*\ln(x)}\]

    • one year ago
  3. juantweaver
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    Is this what you mean?

    • one year ago
  4. Denebel
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    Yes

    • one year ago
  5. juantweaver
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    okay we will need to convert log(x) to ln(x) using a given equation

    • one year ago
  6. juantweaver
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    we are doing this since there are no log(x) in the final answer

    • one year ago
  7. juantweaver
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    \[\log _{a}(x)=\frac{\ln(x)}{\ln(a)}\]

    • one year ago
  8. juantweaver
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    so for log base 10\[\log _{10}(x)=\frac{\ln(x)}{\ln(10)}\]

    • one year ago
  9. juantweaver
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    go ahead and convert this in the expression above. see what you get.

    • one year ago
  10. Denebel
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    |dw:1346315335776:dw|

    • one year ago
  11. juantweaver
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    |dw:1346315440405:dw|

    • one year ago
  12. Denebel
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    ^ How did you get that? Isn't whatever you do to the top, you have to do to the bottom?

    • one year ago
  13. juantweaver
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    you had forgotten the x in the denominator, i simply added it back

    • one year ago
  14. juantweaver
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    \[\frac{\ln(x)}{x*\ln(10)}+\frac{\log(x)}{x}=\frac{\ln(x)}{x*\ln(10)}+\frac{\ln(x)/\ln(10)}{x}\]

    • one year ago
  15. juantweaver
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    then move ln(10) to the denominator of the 2nd fraction

    • one year ago
  16. Denebel
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    where does the log (x) / x come from?

    • one year ago
  17. juantweaver
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    from the original expression that you gave me. you wrote it as \[\log(x)*\frac{1}{x}\]

    • one year ago
  18. juantweaver
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    \[\log(x)*\frac{1}{x}=\frac{\log(x)}{x}\]

    • one year ago
  19. Denebel
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    ? |dw:1346316105596:dw| from this?

    • one year ago
  20. juantweaver
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    yes, unless i was mistaken by what you wrote

    • one year ago
  21. juantweaver
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    \[\ln(x)*\frac{1}{x*\ln(10)}+\log(x)*\frac{1}{x}\] am i misunderstanding what you wrote?

    • one year ago
  22. Denebel
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    Ohh I see it, thank you!

    • one year ago
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