How do you solve $ln x - ln 3 = 2$ $lnx-ln3=2$ ?

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Answer 1 · 2016-02-18T08:31:49

$x = 3 \cdot e^{2}$ $x=3*e^2$

from the given: $ln x - ln 3 = 2$ $ln x-ln 3=2$

$ln (\frac{x}{3}) = 2$ $ln (x/3)=2$

also this means

${ln}_{e} (\frac{x}{3}) = 2$ $ln_e (x/3)=2$

taking the exponential form

$e^{2} = \frac{x}{3}$ $e^2=x/3$

$3 \cdot e^{2} = 3 \cdot \frac{x}{3}$ $3*e^2=3*x/3$ multiplying both sides by 3

$3*e^2=cancel3*x/cancel3$

$3*e^2=x$

and

$color (red)(x=3*e^2)$

Check: at $x=3*e^2$ using the original equation

$ln x-ln 3=2$

$ln 3*e^2-ln 3=2$

$ln ((3*e^2)/3)=2$

$ln (e^2)=2$

$2=2$

How do you solve lnx-ln3=2lnx−ln3=2lnx-ln3=2?