SOLUTION: x∙ln(x)=5, find x

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Question 1151988: x∙ln(x)=5, find x
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x.ln(x)=5, find x!
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Is it x*ln(x) ? Multiplied?
There are no integer solutions to that.
! (factorial) applies only to integers.

Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
The methods of algebra that we study do not apply when a variable 
occurs both within a logarithm expression AND ALSO outside of a 
logarithm expression.  So the only way is to approximate it by
a trial and error process (iterative method) or to use your
graphing calculator such as the TI-83 or TI-84.

On your TI-83 or 84,

Press Y=

Make that screen read:

\Y1=Xln(X)
\Y2=5

Press ZOOM
Press 6

See this graph



Press 2ND
Press TRACE
Press 5

At the bottom of the screen see

First curve?
X=0            Y=

Press the right arrow key about 16 times to get the cursor to
"crawl" up the curve LEFT of the point of intersection, and see
a screen like the one below  It's OK if the values at the bottom of
the screen and different as the cursor crawls up the curve.



Press ENTER three times



Read the answer at the bottom of screen with the graph with the cursor
on the point of intersection:

Intersection
X=3.7686795            Y=5

The answer is that x-value which is 3.7686795

Edwin