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Popular >

e^{2x}-2e^x=15

Solution

e^{2 x} - 2 e^{x} = 15

Solution

x = ln (5)

+1

Decimal Notation

x = 1.60943 \dots

Solution steps

e^{2 x} - 2 e^{x} = 15

Apply exponent rules

(e^{x})^{2} - 2 e^{x} = 15

Rewrite the equation with

e^{x} = u

(u)^{2} - 2 u = 15

Solve

u^{2} - 2 u = 15 : 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 :

No Solution for

x \in R

x = ln (5)

Popular Examples

8^{x} = 0.25

2^{x - 6} = 18

12 \cdot 3^{- x} = \frac{4}{3}

2^{x+1}+2^{x+2}=96

2^{x + 1} + 2^{x + 2} = 96

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

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

Frequently Asked Questions (FAQ)

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