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Popular >

4e^{2x}-5e^x=-1

Solution

4 e^{2 x} - 5 e^{x} = - 1

Solution

x = 0, x = - 2 ln (2)

+1

Decimal Notation

x = 0, x = - 1.38629 \dots

Solution steps

4 e^{2 x} - 5 e^{x} = - 1

Apply exponent rules

4 (e^{x})^{2} - 5 e^{x} = - 1

Rewrite the equation with

e^{x} = u

4 (u)^{2} - 5 u = - 1

Solve

4 u^{2} - 5 u = - 1 : u = 1, u = \frac{1}{4}

u = 1, u = \frac{1}{4}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 1 : x = 0

Solve

e^{x} = \frac{1}{4} : x = - 2 ln (2)

x = 0, x = - 2 ln (2)

Popular Examples

27 = 3^{k}

2^{3 x - 2} = 5

solvefor z,y=e^{-fxz^{2.5}}solve for

z, y = e^{- f x z^{2.5}}

solvefor x,y^2=e^{2x}solve for

x, y^{2} = e^{2 x}

93000*1.0987^x=156500

93000 \cdot 1.098 7^{x} = 156500

Frequently Asked Questions (FAQ)

What is the answer to 4e^{2x}-5e^x=-1 ?
The answer to 4e^{2x}-5e^x=-1 is x=0,x=-2ln(2)