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e^x=2 what is x

 Oct 23, 2014

Best Answer 

 #2
avatar+26397 
+5

 

 

e^x=2 what is x

\boxed{e^x = \ a^ { \dfrac{x}{\ln{(a)}} } = 2^ { \dfrac{x}{\ln{(2)}} }} \\ \\ e^x=2\\\\ 2^ { \textcolor[rgb]{1,0,0}{\dfrac{x}{\ln{(2)}} } } } = 2^\textcolor[rgb]{1,0,0}{1} }\\\\ \textcolor[rgb]{1,0,0}{\dfrac{x}{\ln{(2)}} } } = \textcolor[rgb]{1,0,0}{1} \\\\ x=\ln{(2)}

 Oct 23, 2014
 #1
avatar+130491 
+5

e^x=2 what is x ???

Take the ln of both sides

lnex = ln2       and by  log property, we can write

x lne = ln2     and lne = 1   ....so....

x = ln 2

 

 Oct 23, 2014
 #2
avatar+26397 
+5
Best Answer

 

 

e^x=2 what is x

\boxed{e^x = \ a^ { \dfrac{x}{\ln{(a)}} } = 2^ { \dfrac{x}{\ln{(2)}} }} \\ \\ e^x=2\\\\ 2^ { \textcolor[rgb]{1,0,0}{\dfrac{x}{\ln{(2)}} } } } = 2^\textcolor[rgb]{1,0,0}{1} }\\\\ \textcolor[rgb]{1,0,0}{\dfrac{x}{\ln{(2)}} } } = \textcolor[rgb]{1,0,0}{1} \\\\ x=\ln{(2)}

heureka Oct 23, 2014

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