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