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How do you solve $14 e^{3 x + 2} = 560$ $14e^(3x+2)=560$ ?

1 Answer

Dec 7, 2015

$x = \frac{ln 40 - 2}{3}$ $x= (ln40-2)/3$

Explanation:

If
$XXX 14 e^{3 x + 2} = 560$ $color(white)("XXX")14e^(3x+2) = 560$
then (after dividing both sides by $14$ $14$ )
$XXX e^{3 x + 2} = 40$ $color(white)("XXX")e^(3x+2) = 40$

By taking the natural logarithm of both sides:
$XXX 3 x + 2 = ln 40$ $color(white)("XXX")3x+2 = ln40$

$XXX 3 x = ln 40 - 2$ $color(white)("XXX")3x = ln40-2$

$XXX x = \frac{ln (40) - 2}{3}$ $color(white)("XXX")x = (ln(40)-2)/3$

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