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

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jude69 | Student, Undergraduate | (Level 1) Honors

Posted February 15, 2011 at 11:12 AM via web

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

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted February 15, 2011 at 11:15 AM (Answer #1)

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Given the equation:

ln (lnx) = 4

We need to solve for s.

First we will rewrite in the logarithm form.

==> ln(x) = e^4

Now we will rewrite into the exponent form.

==> x = e^(e^4)

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 15, 2011 at 11:52 AM (Answer #2)

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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 both the sides again

=> x = e^ ( e^4)

The required value of x is e^(e^4).

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tonys538 | TA , Undergraduate | (Level 1) Valedictorian

Posted December 29, 2014 at 11:53 AM (Answer #3)

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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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