Key to "How do you solve for x? e−2x+ex=13?"

Malaki Aguilar

Answered question

2022-02-04

How do you solve for x?

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

Layla Humphrey

Beginner2022-02-05Added 11 answers

Collect

e^{x}

on the left:

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

rearrange:

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

apply the ln on both sides:

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

so:

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

use the properties of log relating sums and subtractions to multiplications and divisions to get:
Therefore,

x = \ln (1) - \ln [3 (e^{- 2} + 1)] = 0 - \ln (3) - \ln (e^{- 2} + 1)

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