Question

trying to solve ln [ ln (ln x)]=1 ? .... I got to ln 0=1?

Answer 1

\[\Large \ln\left[\ln\left(\ln x\right)\right]\quad=\quad 1\]Are you familiar with the process of exponentiation?
Or are you just jumping from log form to exponential form?

Does this process make any sense to you?\[\LARGE e^{\ln\left[\ln\left(\ln x\right)\right]}\quad=\quad e^1\]

Answer 2

I really have not worked log form that much, so I'm fairly familiar but i'm not understanding the base e example? could you simplify? . thank you

Answer 3

The exponential and log function are inverses of one another.
\[\LARGE \color{royalblue}{e}^{\color{royalblue}{\ln}\left[\ln\left(\ln x\right)\right]}\quad=\quad e^1\]So these two functions will essentially "undo" one another.
Simplifying the problem to,\[\Large \ln(\ln x)\quad=\quad e^1\]

Answer 4

Is that a little too confusing?
We can approach the problem a little differently if that doesn't make sense to you.

Answer 5

actually that does, but for some reason i'm wondering if ln (ln 1) =1wouldn't ln 1=0?

Answer 6

Yes ln 1 = 0

But we don't have ln 1 on the inside, we have ln x, don't we? :O

Answer 7

oh, ok. yes, sorry bout that.

Answer 8

This is going to seem like a weird process :)
We're going to repeat what we did before to get rid of the outer log.\[\Large \ln(\ln x)\quad=\quad e\] Exponentiating each side gives us,\[\LARGE e^{\ln(\ln x)}\quad=\quad e^e\]

Answer 9

ok. I think i'm getting it, ln(lnx)=e . so how did it become e^1?

Answer 10

From our initial setup:\[\Large \color{#3366CF}{\ln\left[\ln\left(\ln x\right)\right]\quad=\quad 1}\]We want to rewrite each side as an exponent with a base of e,\[\LARGE e^{\color{#3366CF}{\ln\left[\ln\left(\ln x\right)\right]}}\quad=\quad e^{\color{#3366CF}{1}}\]

Answer 11

Then the left side simplified down,\[\Large \ln\left(\ln x\right)\quad=\quad e^{\color{#3366CF}{1}}\]

Answer 12

aaahhh.... : ) Ok. Crystal Clear, thank you very much. I appreciate it. I'm truly a genius. thanks.

Answer 13

lol :)

Answer 14

You understand where this process is going?
You would have to "exponentiate" 3 times to get to your answer.