anonymous
  • anonymous
How does this simplification work? Can someone show me the intermediate steps?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
|dw:1346313632906:dw|
anonymous
  • anonymous
\[\ln(x)*(\frac{1}{x*\ln10})+\log(x)*(1/x)=\frac{2*\ln(x)}{x*\ln(x)}\]
anonymous
  • anonymous
Is this what you mean?

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anonymous
  • anonymous
Yes
anonymous
  • anonymous
okay we will need to convert log(x) to ln(x) using a given equation
anonymous
  • anonymous
we are doing this since there are no log(x) in the final answer
anonymous
  • anonymous
\[\log _{a}(x)=\frac{\ln(x)}{\ln(a)}\]
anonymous
  • anonymous
so for log base 10\[\log _{10}(x)=\frac{\ln(x)}{\ln(10)}\]
anonymous
  • anonymous
go ahead and convert this in the expression above. see what you get.
anonymous
  • anonymous
|dw:1346315335776:dw|
anonymous
  • anonymous
|dw:1346315440405:dw|
anonymous
  • anonymous
^ How did you get that? Isn't whatever you do to the top, you have to do to the bottom?
anonymous
  • anonymous
you had forgotten the x in the denominator, i simply added it back
anonymous
  • anonymous
\[\frac{\ln(x)}{x*\ln(10)}+\frac{\log(x)}{x}=\frac{\ln(x)}{x*\ln(10)}+\frac{\ln(x)/\ln(10)}{x}\]
anonymous
  • anonymous
then move ln(10) to the denominator of the 2nd fraction
anonymous
  • anonymous
where does the log (x) / x come from?
anonymous
  • anonymous
from the original expression that you gave me. you wrote it as \[\log(x)*\frac{1}{x}\]
anonymous
  • anonymous
\[\log(x)*\frac{1}{x}=\frac{\log(x)}{x}\]
anonymous
  • anonymous
? |dw:1346316105596:dw| from this?
anonymous
  • anonymous
yes, unless i was mistaken by what you wrote
anonymous
  • anonymous
\[\ln(x)*\frac{1}{x*\ln(10)}+\log(x)*\frac{1}{x}\] am i misunderstanding what you wrote?
anonymous
  • anonymous
Ohh I see it, thank you!

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