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



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Denebel
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dw:1346313632906:dw

juantweaver
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\[\ln(x)*(\frac{1}{x*\ln10})+\log(x)*(1/x)=\frac{2*\ln(x)}{x*\ln(x)}\]

juantweaver
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Is this what you mean?

Denebel
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Yes

juantweaver
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okay we will need to convert log(x) to ln(x) using a given equation

juantweaver
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we are doing this since there are no log(x) in the final answer

juantweaver
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\[\log _{a}(x)=\frac{\ln(x)}{\ln(a)}\]

juantweaver
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so for log base 10\[\log _{10}(x)=\frac{\ln(x)}{\ln(10)}\]

juantweaver
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go ahead and convert this in the expression above. see what you get.

Denebel
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dw:1346315335776:dw

juantweaver
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dw:1346315440405:dw

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?

juantweaver
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you had forgotten the x in the denominator, i simply added it back

juantweaver
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\[\frac{\ln(x)}{x*\ln(10)}+\frac{\log(x)}{x}=\frac{\ln(x)}{x*\ln(10)}+\frac{\ln(x)/\ln(10)}{x}\]

juantweaver
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then move ln(10) to the denominator of the 2nd fraction

Denebel
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where does the log (x) / x come from?

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

juantweaver
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\[\log(x)*\frac{1}{x}=\frac{\log(x)}{x}\]

Denebel
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? dw:1346316105596:dw from this?

juantweaver
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yes, unless i was mistaken by what you wrote

juantweaver
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\[\ln(x)*\frac{1}{x*\ln(10)}+\log(x)*\frac{1}{x}\]
am i misunderstanding what you wrote?

Denebel
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Ohh I see it, thank you!