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Popular >

e^{2x}-5e^x=-6

Solution

e^{2 x} - 5 e^{x} = - 6

Solution

x = ln (3), x = ln (2)

+1

Decimal Notation

x = 1.09861 \dots, x = 0.69314 \dots

Solution steps

e^{2 x} - 5 e^{x} = - 6

Apply exponent rules

(e^{x})^{2} - 5 e^{x} = - 6

Rewrite the equation with

e^{x} = u

(u)^{2} - 5 u = - 6

Solve

u^{2} - 5 u = - 6 : u = 3, u = 2

u = 3, u = 2

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

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

x = ln (3), x = ln (2)

Popular Examples

e^{2 x + 1} = 3

e^{- x} = \frac{1}{2}

e^{6x}+10e^{3x}-11=0

e^{6 x} + 10 e^{3 x} - 11 = 0

(\frac{1}{3})^{x} = 27

11 \cdot 1 0^{5 t} = 20

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-5e^x=-6 ?
The answer to e^{2x}-5e^x=-6 is x=ln(3),x=ln(2)