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Popular >

e^{2x}+3e^x-10=0

Solution

e^{2 x} + 3 e^{x} - 10 = 0

Solution

x = ln (2)

+1

Decimal Notation

x = 0.69314 \dots

Solution steps

e^{2 x} + 3 e^{x} - 10 = 0

Apply exponent rules

(e^{x})^{2} + 3 e^{x} - 10 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} + 3 u - 10 = 0

Solve

u^{2} + 3 u - 10 = 0 : u = 2, u = - 5

u = 2, u = - 5

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 2 : x = ln (2)

Solve

e^{x} = - 5 :

No Solution for

x \in R

x = ln (2)

Popular Examples

2(2^2)^x-10(2^x)+12=0

2 (2^{2})^{x} - 10 (2^{x}) + 12 = 0

5^{x-2}=3^{3x+2}

5^{x - 2} = 3^{3 x + 2}

3^{2 x} = 9

2^{5x}=3^{2x+1}

2^{5 x} = 3^{2 x + 1}

2^{x - 1} = 1

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}+3e^x-10=0 ?
The answer to e^{2x}+3e^x-10=0 is x=ln(2)