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Popular >

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

Solution

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

Solution

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

+1

Decimal Notation

x = - 0.61819 \dots

Solution steps

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

Rewrite the equation with

e^{- 3 x} = u

ln (1 + u) = 2

Solve

ln (1 + u) = 2 : u = e^{2} - 1

u = e^{2} - 1

Substitute back

u = e^{- 3 x},

solve for

x

Solve

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

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

Popular Examples

4^{x} = 15

7^{x-10}+7^{x-9}+7^{x-8}=57

7^{x - 10} + 7^{x - 9} + 7^{x - 8} = 57

3^{y^{2} - 3 y} = 81

5^{x} + 5^{- x} = 6

9^{3x+1}=3^{4x+10}

9^{3 x + 1} = 3^{4 x + 10}

Frequently Asked Questions (FAQ)

What is the answer to ln(1+e^{-3x})=2 ?
The answer to ln(1+e^{-3x})=2 is x=-(ln(e^2-1))/3