# How do you find the limit of #(ln (ln (x) ) ) / ( ln (x) ) # as x approaches #1#?

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To find the limit of (ln(ln(x))) / (ln(x)) as x approaches 1, we can use L'Hôpital's Rule. Taking the derivative of the numerator and denominator separately, we get:

d/dx (ln(ln(x))) = 1 / (x * ln(x)) d/dx (ln(x)) = 1 / x

Now, we can evaluate the limit by substituting x = 1:

lim(x→1) (ln(ln(x))) / (ln(x)) = lim(x→1) (1 / (x * ln(x))) / (1 / x) = lim(x→1) (1 / (x * ln(x))) * (x / 1) = lim(x→1) 1 / ln(x) = 1 / ln(1) = 1 / 0 = undefined

Therefore, the limit of (ln(ln(x))) / (ln(x)) as x approaches 1 is undefined.

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