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Popular >

2e^{2x}-7e^x+3=0

Solution

2 e^{2 x} - 7 e^{x} + 3 = 0

Solution

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

+1

Solution steps

2 e^{2 x} - 7 e^{x} + 3 = 0

Apply exponent rules

2 (e^{x})^{2} - 7 e^{x} + 3 = 0

Rewrite the equation with

e^{x} = u

2 (u)^{2} - 7 u + 3 = 0

Solve

2 u^{2} - 7 u + 3 = 0 : u = 3, u = \frac{1}{2}

u = 3, u = \frac{1}{2}

Substitute back

u = e^{x},

solve for

x

Solve

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

Solve

e^{x} = \frac{1}{2} : x = - ln (2)

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

Popular Examples

2^{2x^2-2}-8^x=0

2^{2 x^{2} - 2} - 8^{x} = 0

4^{x - 1} = 7

4^{x - 1} = 1

9^{x + 1} = 27

3^{2x+5}=27^{x-1}

3^{2 x + 5} = 2 7^{x - 1}

Frequently Asked Questions (FAQ)

What is the answer to 2e^{2x}-7e^x+3=0 ?
The answer to 2e^{2x}-7e^x+3=0 is x=ln(3),x=-ln(2)