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Popular >

e^{2x}-8e^x+15=0

Solution

e^{2 x} - 8 e^{x} + 15 = 0

Solution

x = ln (5), x = ln (3)

+1

Decimal Notation

x = 1.60943 \dots, x = 1.09861 \dots

Solution steps

e^{2 x} - 8 e^{x} + 15 = 0

Apply exponent rules

(e^{x})^{2} - 8 e^{x} + 15 = 0

Rewrite the equation with

e^{x} = u

(u)^{2} - 8 u + 15 = 0

Solve

u^{2} - 8 u + 15 = 0 : u = 5, u = 3

u = 5, u = 3

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

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

x = ln (5), x = ln (3)

Popular Examples

200 = 100 e^{r \cdot 6}

2^{x} = 24

x^{sqrt(x)}=sqrt(x^x)

x^{x} = x^{x}

4^{2x}-4^x-12=0

4^{2 x} - 4^{x} - 12 = 0

2^{x + 1} = 16

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-8e^x+15=0 ?
The answer to e^{2x}-8e^x+15=0 is x=ln(5),x=ln(3)