How do you solve $\frac{119}{e^{6 x} - 14} = 7$ $119/(e^(6x)-14)=7$ ?

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How do you solve $\frac{119}{e^{6 x} - 14} = 7$ $119/(e^(6x)-14)=7$ ?

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Answer 1 · 2017-01-18T15:16:15

$x = \frac{1}{6} ln 31$ $x=1/6ln31$

Explanation:

$\frac{119}{e^{6 x} - 14} = 7$ $frac{119}{e^(6x)-14}=7$

Multiply each side by $(e^{6 x} - 14) :$ $(e^(6x)-14):$
$119 = 7 (e^{6 x} - 14)$ $119=7(e^(6x)-14)$

Divide each side by 7:
$17 = e^{6 x} - 14$ $17=e^(6x)-14$

Add 14 to each side:
$31 = e^{6 x}$ $31=e^(6x)$

Take the natural log of each side:
$ln (31) = ln (e^{6 x})$ $ln(31)=ln(e^(6x))$

$6 x = ln 31$ $6x=ln31$

Divide each side by 6:
$x = \frac{1}{6} ln 31$ $x=1/6ln31$

Check answer by confirming $e^(6x)-14 cancel=0$ (Make sure denominator of original equation is not zero)
$e^(6x)=14$
$6x=ln14$
$x=1/6ln14$
$1/6ln31cancel=ln14$

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How do you solve $\frac{119}{e^{6 x} - 14} = 7$ $119/(e^(6x)-14)=7$ ?

1 Answer

Explanation:

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