How do you solve $2 e^{3 x} = 4 e^{5 x}$ $2e^(3x) = 4e^(5x)$ ?

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Answer 1 · 2016-01-18T01:38:36

Start by dividing both sides by $4 e^{3 x}$ $4e^(3x)$ ...

$2 e^{3 x} = 4 e^{5 x}$ $2e^(3x) = 4e^(5x)$

Divide both sides by $4 e^{3 x}$ $4e^(3x)$ ...

$\frac{1}{2} = e^{2 x}$ $1/2=e^(2x)$

Now take the natural log of both sides ...

$ln (\frac{1}{2}) = ln (e^{2 x}) = 2 x$ $ln(1/2)=ln(e^(2x))=2x$

$x = \frac{ln (\frac{1}{2})}{2} = \frac{- ln 2}{2} \approx - 0.3466$ $x=ln(1/2)/2=(-ln2)/2~~-0.3466$

hope that helped

How do you solve 2e3x=4e5x2e^(3x) = 4e^(5x)?