What is the answer to 2e^x=7sqrt(e^x)-3 ?

The answer to 2e^x=7sqrt(e^x)-3 is x=2ln(3),x=-2ln(2)

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2e^x=7sqrt(e^x)-3

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

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

Solution steps

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

Rewrite the equation with

e^{x} = u

2 u = 7 u - 3

Solve

2 u = 7 u - 3 : u = 9, u = \frac{1}{4}

u = 9, u = \frac{1}{4}

Substitute back

u = e^{x},

solve for

x

Solve

e^{x} = 9 : x = 2 ln (3)

Solve

e^{x} = \frac{1}{4} : x = - 2 ln (2)

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

\frac{1}{64} = 2^{x}

12 5^{x - 1} = 2 5^{x}

x, x y e^{\frac{y}{x}} = 5

9^{3 x} = 2 7^{x + 2}

5^{- x} = 3. 5^{3 x}

What is the answer to 2e^x=7sqrt(e^x)-3 ?
The answer to 2e^x=7sqrt(e^x)-3 is x=2ln(3),x=-2ln(2)