How do you solve $3 + 2 ln x = 10$ ?

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Answer 1 · 2015-08-12T23:46:12

$color(red)( x=e^(7/2))$

$3+2lnx=10$

Subtract $3$ from each side.

$2lnx=7$

Divide each side by $2$ .

$lnx=7/2$

Convert the logarithmic equation to an exponential equation.

$e^lnx = e^(7/2)$

Remember that $e^lnx =x$ , so

$x=e^(7/2)$

Check:

$3+2lnx=10$

If $x= e^(7/2)$ ,

$3+2lne^(7/2)=10$

$3+2(7/2)=10$

$3+7=10$

$10=10$

$x=e^(7/2)$ is a solution.

How do you solve 3 + 2 ln x = 103 + 2 ln x = 10?