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Find the value of a if,lim_(xto0)(e^(ax)-e^x)/x=2

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SOLUTION :`lim_(xto0)(e^(ax)-e^x)/x=2`
`implieslim_(xto0){(e^(ax)-1)/x-(e^x-1)/x}=2`
`implieslim_(xto0){a(e^(ax)-1)/(ax)-(e^x-1)/x}=2`
`impliesalim_(xto0)(e^(ax)-1)/(ax)-lim_(xto0)(e^x-1)/x=2`
`a-1=2impliesa=3`


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