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Popular >

e^{2x}-4e^x-21=0

Solution

e^{2 x} - 4 e^{x} - 21 = 0

Solution

x = ln (7)

+1

Decimal Notation

x = 1.94591 \dots

Solution steps

e^{2 x} - 4 e^{x} - 21 = 0

Apply exponent rules

(e^{x})^{2} - 4 e^{x} - 21 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 4 u - 21 = 0

Solve

u^{2} - 4 u - 21 = 0 : u = 7, u = - 3

u = 7, u = - 3

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 7 : x = ln (7)

Solve

e^{x} = - 3 :

No Solution for

x \in R

x = ln (7)

Popular Examples

3^{(4-x)}=27^{(2-x)}

3^{(4 - x)} = 2 7^{(2 - x)}

solvefor y,x^y=N solve for

y, x^{y} = N

3^{x - 2} = 11

solvefor x,3^x= 1/81 solve for

x, 3^{x} = \frac{1}{81}

solvefor x,y^2=e^{2x}+2x+c solve for

x, y^{2} = e^{2 x} + 2 x + c

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-4e^x-21=0 ?
The answer to e^{2x}-4e^x-21=0 is x=ln(7)