Solve analytically:
e^x=x+3
If you do not know how - the title of this puzzle might guide you.
If we call the Lambert function w elementary, this can indeed be solved analytically. w is defined as the inverse of x -> x*e^x and has branches w_0 and w_-1 in the real numbers.
e^x = x+3
<=>
e^-3*e^(x+3) = x+3
<=>
-e^-3 = -(x+3)*e^-(x+3)
Now apply the w function on both sides:
w_i(-e^-3) = -(x+3), i=0,-1
<=>
x = -3-w_i(-e^-3), i=0,-1
I am not showing you the numerical values, we seek, after all, an analytical solution.
Edited on January 23, 2020, 12:36 pm
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Posted by JLo
on 2020-01-23 12:34:40 |
No Subject