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Popular >

0=-e^{-x}+3e^{-3x}

Solution

0 = - e^{- x} + 3 e^{- 3 x}

Solution

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

+1

Decimal Notation

x = 0.54930 \dots

Solution steps

0 = - e^{- x} + 3 e^{- 3 x}

Add

e^{- x}

to both sides

0 + e^{- x} = - e^{- x} + 3 e^{- 3 x} + e^{- x}

Simplify

e^{- x} = 3 e^{- 3 x}

Apply exponent rules

- x = ln (3) - 3 x

Solve

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

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

Popular Examples

2^{\frac{x}{15}} = 10

x=e^{((xln(2)))/2}

x = e^{\frac{( x l n ( 2 ) )}{2}}

49^x*7^{x^2}=2401^2

4 9^{x} \cdot 7^{x^{2}} = 240 1^{2}

2500=5000e^{100x}

2500 = 5000 e^{100 x}

3^{2 x} = 2

Frequently Asked Questions (FAQ)

What is the answer to 0=-e^{-x}+3e^{-3x} ?
The answer to 0=-e^{-x}+3e^{-3x} is x=(ln(3))/2