How do you solve $2 ln x - ln 3 = 2$ $2 ln x - ln 3 = 2$ ?

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How do you solve $2 ln x - ln 3 = 2$ $2 ln x - ln 3 = 2$ ?

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Answer 1 · 2016-06-14T02:10:55

I found: $x = 4.7082$ $x=4.7082$

Explanation:

We can write it as:
${ln x}^{2} - ln 3 = 3$ $lnx^2-ln3=3$
then:
$ln (\frac{x^{2}}{3}) = 2$ $ln(x^2/3)=2$
use the definition of log:
$\frac{x^{2}}{3} = e^{2}$ $x^2/3=e^2$
$x^{2} = 3 e^{2}$ $x^2=3e^2$
$x = \pm \sqrt{3 e^{2}}$ $x=+-sqrt(3e^2)$
we accept only the positive one:
$x = \sqrt{3 e^{2}} = 4.7082$ $x=sqrt(3e^2)=4.7082$

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How do you solve $2 ln x - ln 3 = 2$ $2 ln x - ln 3 = 2$ ?

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