Solve x if ln(ln(x)) = 4

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justaguide eNotes educator | Certified Educator

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We have ln (ln (x)) = 4

ln x has a base of e.

Taking the antilog of both the sides

=> ln (x ) = e^ 4

Taking the antilog of...

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tonys538 | Student

The logarithmic equation `ln(ln(x)) = 4` has to be solved for x.

ln is used to denote natural logarithm which is logarithm to the base e.

`ln(ln(x)) = 4` can be rewritten as:

`log_e(log_ex) = 4`

If `log_b a = c` , we can write `a = b^c`

This gives: `log_e x = e^4`

Again doing the same.

`x = e^(e^4)`

The root of the equation `ln(ln(x)) = 4` is `x = e^(e^4)`

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