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Popular >

e^{2x}-8e^x=20

Solution

e^{2 x} - 8 e^{x} = 20

Solution

x = ln (10)

+1

Decimal Notation

x = 2.30258 \dots

Solution steps

e^{2 x} - 8 e^{x} = 20

Apply exponent rules

(e^{x})^{2} - 8 e^{x} = 20

Rewrite the equation with

e^{x} = u

(u)^{2} - 8 u = 20

Solve

u^{2} - 8 u = 20 : u = 10, u = - 2

u = 10, u = - 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 10 : x = ln (10)

Solve

e^{x} = - 2 :

No Solution for

x \in R

x = ln (10)

Popular Examples

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y, ln (x) + e^{- \frac{y}{x}} = c

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3^{x + 1} + 3^{x - 1} = 30

2e^{8x}+e^{4x}-1=0

2 e^{8 x} + e^{4 x} - 1 = 0

125 = 5^{x}

10^{2x+9}=6*7^{x-4}

1 0^{2 x + 9} = 6 \cdot 7^{x - 4}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-8e^x=20 ?
The answer to e^{2x}-8e^x=20 is x=ln(10)