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Popular >

e^{2x}-2e^x-24=0

Solution

e^{2 x} - 2 e^{x} - 24 = 0

Solution

x = ln (6)

+1

Decimal Notation

x = 1.79175 \dots

Solution steps

e^{2 x} - 2 e^{x} - 24 = 0

Apply exponent rules

(e^{x})^{2} - 2 e^{x} - 24 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 2 u - 24 = 0

Solve

u^{2} - 2 u - 24 = 0 : u = 6, u = - 4

u = 6, u = - 4

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 6 : x = ln (6)

Solve

e^{x} = - 4 :

No Solution for

x \in R

x = ln (6)

Popular Examples

e^{x - 2} = 1

3^{2x}-12(3^x)+27=0

3^{2 x} - 12 (3^{x}) + 27 = 0

1+9^X=3^{X+1}+3^{X-1}

1 + 9^{X} = 3^{X + 1} + 3^{X - 1}

2^{3x+4}=2^{2x}

2^{3 x + 4} = 2^{2 x}

2^{x} = 8^{3}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-2e^x-24=0 ?
The answer to e^{2x}-2e^x-24=0 is x=ln(6)