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Find the value of lim(x to 1) (log3 3x)^...

Find the value of `lim_(x to 1) (log_3 3x)^(log_x 3)`

Text Solution

Verified by Experts

The correct Answer is:
`e`
`underset(xtooo)lim(log_(3)3x)^(log_(x)3)=underset(xto1)lim(log_(3)+log_(3)x)^((1)/(log_(3)x))`
`=underset(xto1)lim(1+log_(3)x)^((1)/(log_(3)x))" "(1^(oo)"form")`
=e
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