What is the value of x in the equation below 1 + 2e^{x + 1} = 9

Solution:

Given, equation is

1 + 2e^{x + 1} = 9

2e^{x + 1} = 9 - 1

2e^{x + 1} = 8

e^{x + 1} = 8/2

e^{x + 1} = 4

Taking log natural (ln) on both sides we have

ln(e^{x + 1}) = ln(4)

We know that ln(a)ⁿ = nloga, therefore

(x + 1)ln(e) = ln4

ln(e) = 1, therefore

x + 1 = ln4

x + 1 = 1.3863

x = 1.3863 - 1

x = 0.3863

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What is the value of x in the equation below 1 + 2e^{x + 1} = 9

Summary:

 The value of x in the equation 1 + 2e^{x + 1} = 9 is 0.3863