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# How do you simplify e^lnx?

Mar 22, 2016

${e}^{\ln} x = x$
let $y = {e}^{\ln} x$
$\ln y = \ln {e}^{\ln} x$->Take ln of both sides
$\ln y = \ln x \cdot \ln e$ -> use the property ${\log}_{b} {x}^{n} = n {\log}_{b} x$
$\ln y = \ln x \left(1\right)$-> ${\ln}_{e} e = 1$-> from the property ${\log}_{b} b = 1$
$\ln y = \ln x$
Therefore $y = x$