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Popular >

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

Solution

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

Solution

x = ln (5)

+1

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 = 5, u = - 2

u = 5, u = - 2

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 5 : x = ln (5)

Solve

e^{x} = - 2 :

No Solution for

x \in R

x = ln (5)

Popular Examples

9^{x-1}=(1/3)^{2x}

9^{x - 1} = (\frac{1}{3})^{2 x}

4-(6^{5-3x})=-5

4 - (6^{5 - 3 x}) = - 5

e^{2 x} + e^{x} = 12

1 6^{x} = 8

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

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

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(5)