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Popular >

e^{2x}+e^x=6

Solution

e^{2 x} + e^{x} = 6

Solution

x = ln (2)

+1

Decimal Notation

x = 0.69314 \dots

Solution steps

e^{2 x} + e^{x} = 6

Apply exponent rules

(e^{x})^{2} + e^{x} = 6

Rewrite the equation with

e^{x} = u

(u)^{2} + u = 6

Solve

u^{2} + u = 6 : u = 2, u = - 3

u = 2, u = - 3

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = - 3 :

No Solution for

x \in R

x = ln (2)

Popular Examples

e^{x+2}=(e^{x-1})^2

e^{x + 2} = (e^{x - 1})^{2}

1 6^{x} = 128

3^{2x}+3^{x+1}=18

3^{2 x} + 3^{x + 1} = 18

3^{2x+1}-28(3^x)+9=0

3^{2 x + 1} - 28 (3^{x}) + 9 = 0

x^x=\sqrt[4]{2}

Frequently Asked Questions (FAQ)

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