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Could someone show work for why $e^{2\ln(x)}$ = $x^2$ ? I ran across this while solving an ODE but have completely forgotten the rules used here. I hate to ask it, but i'd rather ask it this once than go on in ignorance.

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$2\ln{x}=\ln{x^2}$ so $e^{2\ln x}=e^{\ln x^2}= x^2$

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  • $\begingroup$ Please note that this identity is only true on the respective domains on either side of the equal sign. So technically, only for $x>0$ $\endgroup$
    – imranfat
    Sep 1, 2014 at 21:35
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$$ a^{bc} = \Big(a^b\Big)^c = \Big(c^c\Big)^b $$ $$ e^{2\ln x} =\Big(e^{\ln x}\Big)^2 = \Big(x\Big)^2. $$

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