Solving Logarithm Overkill: Find Exact Value for ln(ln[e^{e^{5}}])

[danielle36]

Hello again!
I have been working on this log, and the longer I work on it, the more confused I get! Here's the problem:
Find the exact value for:

$$ln(ln[e^{e^{5}}$$])

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Here's what I've tried so far:

$$e(ln[e^{e^5}}$$])

$$e^{x} = ln(e^{e^5}})$$
$$e^{x} = e^{e^5}}$$
$$e^{5} = (2.72)^{5}$$
$$e^{x} = e^{149}$$
$$x = 149$$

...I have no idea if I'm doing this right, but I'm not feeling like I am...Help?

 

[Midy1420]

use the property that Ln(a^b) = b Ln(a), Ln(e) = 1, Ln(e^a) = a

 

[rock.freak667]

z=ln(lne^(e^5)). Use the definition of a log now.