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

Mathematics
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|dw:1346313632906:dw|
\[\ln(x)*(\frac{1}{x*\ln10})+\log(x)*(1/x)=\frac{2*\ln(x)}{x*\ln(x)}\]
Is this what you mean?

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Other answers:

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

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