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How do you solve $ln 4 - ln x = 10$ $ln4-lnx=10$ ?

1 Answer

Nov 29, 2015

$x = \frac{4}{e^{10}} = \approx 1.82 \times 10^{- 4}$ $x=4/(e^10)=~~1.82xx10^(-4)$

Explanation:

$ln (4) - ln (x) = 10$ $ln(4) - ln(x) =10$

$XXXXXXXXXX$ $color(white)("XXXXXXXXXX")$ since $log (\frac{a}{b}) = log (a) - log (b)$ $log(a/b) = log(a)-log(b)$
$\Rightarrow ln (\frac{4}{x}) = 10$ $rArr ln(4/x) = 10$

$XXXXXXXXXX$ $color(white)("XXXXXXXXXX")$ taking each side of the above as an exponent of $e$ $e$
$\Rightarrow \frac{4}{x} = e^{10}$ $rArr 4/x = e^10$

$XXXXXXXXXX$ $color(white)("XXXXXXXXXX")$ algebraic simplification
$\Rightarrow x = \frac{4}{e^{10}}$ $rArr x = 4/(e^10)$

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