What is the answer to 5e^{2ln(x)}+14e^{ln(x)}=3 ?

The answer to 5e^{2ln(x)}+14e^{ln(x)}=3 is x= 1/5

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5e^{2ln(x)}+14e^{ln(x)}=3

5 e^{2 l n (x)} + 14 e^{l n (x)} = 3

x = \frac{1}{5}

Solution steps

5 e^{2 l n (x)} + 14 e^{l n (x)} = 3

Factor

5 e^{2 l n (x)} + 14 e^{l n (x)} : e^{l n (x)} (5 e^{l n (x)} + 14)

e^{l n (x)} (5 e^{l n (x)} + 14) = 3

Rewrite the equation with

e^{l n (x)} = u

u (5 u + 14) = 3

Solve

u (5 u + 14) = 3 : u = \frac{1}{5}, u = - 3

u = \frac{1}{5}, u = - 3

Substitute back

u = e^{l n (x)},

solve for

x

Solve

e^{l n (x)} = \frac{1}{5} : x = \frac{1}{5}

Solve

e^{l n (x)} = - 3 :

No Solution for

x \in R

x = \frac{1}{5}

32 + 2^{x - 1} = 2^{x}

e^{2 x + 1} = 9 e^{1 - x}

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

3^{2 x - 1} = 9^{x - 2}

133.9 = \frac{133.9}{1 + 2 e ^{- x}}

What is the answer to 5e^{2ln(x)}+14e^{ln(x)}=3 ?
The answer to 5e^{2ln(x)}+14e^{ln(x)}=3 is x= 1/5