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Popular >

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

Solution

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

Solution

x = ln (3)

+1

Decimal Notation

x = 1.09861 \dots

Solution steps

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

Apply exponent rules

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

Rewrite the equation with

e^{x} = u

(u)^{2} + u = 12

Solve

u^{2} + u = 12 : u = 3, u = - 4

u = 3, u = - 4

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 3 : x = ln (3)

Solve

e^{x} = - 4 :

No Solution for

x \in R

x = ln (3)

Popular Examples

1 6^{x} = 8

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

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

7^{3-x}=5^{x+1}

7^{3 - x} = 5^{x + 1}

4^{x+5}-4^{x+4}=384

4^{x + 5} - 4^{x + 4} = 384

3^{1-x^2}= 1/27

3^{1 - x^{2}} = \frac{1}{27}

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}+e^x=12 ?
The answer to e^{2x}+e^x=12 is x=ln(3)