$e^{x}$ $e^x$ + $ln x$ $lnx$ + $2 x$ $2x$ = $3$ $3$ Find all possible values of x.?

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Answer 1 · 2018-07-19T15:06:23

There is only one solution $x = 0.69$ $x=0.69$

Let

$f (x) = e^{x} + ln x + 2 x - 3$ $f(x)=e^x+lnx+2x-3$

Then,

$f'(x)=e^x+1/x+2$

Apply Newton-Raphson Method

$x_(n+1)=x_n-f(x_n)/(f'(x_n))$

Let $x_0=1$

Then,

$x_1=1-f(1)/(f'(1))=0.816325$

$x_2=0.816325-f(0.816325)/(f'(0.816325))=0.69235$

$x_3=0.69235-f(0.692355)/(f'(0.692355))=0.69178$

graph{e^x+ln(x)+2x-3 [-4.933, 4.934, -2.465, 2.467]}

e^xexe^x+lnxlnxlnx+2x2x2x=333 Find all possible values of x.?