I need help to solve for x:
ln(x) = 6.76876

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Clarification of Question by worldanh-ga on 05 Apr 2006 23:36 PDT

please show work

Well using a log law where:
log to the base e (ln)x=6.76876 is the same as e^6.76876=x that is
your answer, sounds a bit like homework to me though.

I couldn't find the law to solve for x, I just made up a number so
it's easier to phrase the question. Thanks that's what I need

You may already know that you can put skywayman's answer, e^6.76876,
into the google search bar and get the numerical result.

Brix, nwhy answer isnt numerical? e is an actual number, just an
irrational number so it is easier to leave it as e, but by all measn
find an approximation.

ln is the standard logarithm with the natural base (e).

The exponential function (f(x) = e^x) is the inverse of the natural
logarithm (f(x) = ln(x)).

Ergo

ln(e^x) = x and e^(ln(x)) = x

Therefore just take the exponential of both sides and you have x = e^6.76876.

All of this follows from the definition of the logarithm (inverse of exponential).

My apologies, skywalkman, I should have said that if worldanh wanted
"to convert skywalkman's answer to a decimal number, the google search
box would do it."

The math capabilities of the google search box were what interested me
because 1) the search bar is often more accessible than a calculator
and I, myself, sometimes forget the search bar capabilities 2) it
hadn't occurred to me (prior to this problem) to see if the search bar
would handle a term like e^6.76876.

Your answer comes directly from the basics of natural logarithm.
You define natural logarithm as ::
e^ln(x) = x     for all positive x and 
ln(e^x) = x     for all real x. 
where e = 2.7182818284590452353602874713527.

So when u need to solve :: ln(x) = 6.76876
                        =>    x  = e^6.76876
                        =>    x  = 870.23213683001662461830963958677

like to solve for logx = 89, you would do 10^89 = 1x10^89