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Mathematics 33 Online
OpenStudy (rainbow_dash):

evaluate e^(ln y)

OpenStudy (amistre64):

e cancels ln

OpenStudy (ash2326):

@Rainbow_Dash We have \[\large e^{\ln y}\] We know \(\ln x=\log_e x\) \[\large e^{\log_e y}\] there is a logarithmic property \[\large a^{\log_a b}=b\] using that, we get \[\large e^{\log_e y}=y\]

OpenStudy (asnaseer):

one way of looking at this is to let:\[\ln(y)=x\]this implies:\[y=e^x\tag{1}\]therefore:\[e^{\ln(y)}=e^x=y\text{ using(1)}\]

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