Get the answer to "How do you solve for x? e−2x=13?"

Reina Pennington

Answered question

2022-02-04

How do you solve for x?

e^{- 2 x} = \frac{1}{3} ?

Ijezid8t

Beginner2022-02-05Added 13 answers

Step 1
Convert the equation to logarithm form.

e^{- 2 x} = \frac{1}{3}

\Leftrightarrow \log_{e} (\frac{1}{3}) = - 2 x

\ln (\frac{1}{3}) = - 2 x

Isolate x.

(- \frac{1}{2}) [\ln (\frac{1}{3})] = (- \frac{1}{2}) (- 2 x)

P S K \frac{- \ln (\frac{1}{3})}{2} = x

Simplify.

\frac{\ln ({(\frac{1}{3})}^{- 1})}{2} = x

Theorem: Logarithm of a Power

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

You can leave the answer at that since you can't really get

\ln (3)

without a calculator.
The actual answer is around 0.54930614433.

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