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Popular >

e^{2x}-7e^x=-10

Solution

e^{2 x} - 7 e^{x} = - 10

Solution

x = ln (5), x = ln (2)

+1

Decimal Notation

x = 1.60943 \dots, x = 0.69314 \dots

Solution steps

e^{2 x} - 7 e^{x} = - 10

Apply exponent rules

(e^{x})^{2} - 7 e^{x} = - 10

Rewrite the equation with

e^{x} = u

(u)^{2} - 7 u = - 10

Solve

u^{2} - 7 u = - 10 : u = 5, u = 2

u = 5, u = 2

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

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

x = ln (5), x = ln (2)

Popular Examples

5^{x^{2} + x} = 25

2e^{3y+8}-11e^{5-10y}=0

2 e^{3 y + 8} - 11 e^{5 - 10 y} = 0

2^{4 x - 2} = 3

4^{x} = 6^{x + 2}

3 6^{x} = 6

Frequently Asked Questions (FAQ)

What is the answer to e^{2x}-7e^x=-10 ?
The answer to e^{2x}-7e^x=-10 is x=ln(5),x=ln(2)