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OpenStudy (anonymous):
Let u=log x
OpenStudy (anonymous):
2^logx
OpenStudy (anonymous):
logx = e^( log (log(x) )
myininaya (myininaya):
\[\int\limits_{}^{}2^{logx}dx\]
OpenStudy (anonymous):
ya dats true myininaya
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myininaya (myininaya):
i was just writing it the way i like to see it lol
OpenStudy (anonymous):
e^(log(2) ) =2
OpenStudy (anonymous):
so 2^log(x) = [ e^(log(2) ) ]^ log(x)
OpenStudy (anonymous):
= e^[(log2)(logx)]
OpenStudy (anonymous):
not sure if its getting anywhere
but its similiar to integrating or differentiating something like 2^x
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OpenStudy (blacksteel):
You've got the solution right there elec.
2^log(x) = [ e^(log(2) ) ]^ log(x) = [ e^(log(x) ) ]^ log(2) = x^log(2) = x ^(log(2) + 1)/(log(2) + 1)
OpenStudy (blacksteel):
or x*x^log(2) / [1 + log(2)]
OpenStudy (anonymous):
2^logx = x^log2 solve it !!
OpenStudy (anonymous):
\[2^{logx} = x ^{\log2} \]
substitute this n ull find the integral of the form \[x ^{?}\]
OpenStudy (anonymous):
blacksteel can u just give me the correct explanation for this??i meant step by step?
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OpenStudy (anonymous):
Use this old trick that is usually used for the derivative and apply it to the integral. Let\[y =2^{\log x}\]\[\ln y =(\log x)(\ln 2) \]Take integral both sides. It becomes integral of log x with the coefficient ln 2.