What is the answer to x4*3^{3x+2}+3^{3x+3}=7 ?

The answer to x4*3^{3x+2}+3^{3x+3}=7 is x=(4\W_{0}((21e^{\frac{ln(3))/4}ln(3))/(4))-9ln(3)}{12ln(3)}

Solve for x: x4*3^{3x+2}+3^{3x+3}=7

The solution is x=(4\W_{0}((21e^{\frac{ln(3))/4}ln(3))/(4))-9ln(3)}{12ln(3)}

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x 4 \cdot 3^{3 x + 2} + 3^{3 x + 3} = 7

x = \frac{4 W _{0} ( \frac{21 e ^{\frac{l n ( 3 )}{4}} l n ( 3 )}{4} ) - 9 ln ( 3 )}{12 ln ( 3 )}

Solution steps

x \cdot 4 \cdot 3^{3 x + 2} + 3^{3 x + 3} = 7

Prepare

x 4 \cdot 3^{3 x + 2} + 3^{3 x + 3} = 7

for Lambert form:

e^{l n (3) (2 + 3 x)} (4 x + 3) = 7

Rewrite the equation with

(3 x + \frac{9}{4}) ln (3) = u

and

x = \frac{4 u - 9 ln ( 3 )}{12 ln ( 3 )}

e^{l n (3) (2 + 3 (\frac{4 u - 9 l n ( 3 )}{12 l n ( 3 )}))} (4 (\frac{4 u - 9 ln ( 3 )}{12 ln ( 3 )}) + 3) = 7

Simplify

e^{2 l n (3) + \frac{4 u - 9 l n ( 3 )}{4}} (\frac{4 u - 9 ln ( 3 )}{3 ln ( 3 )} + 3) = 7

Rewrite

e^{2 l n (3) + \frac{4 u - 9 l n ( 3 )}{4}} (\frac{4 u - 9 ln ( 3 )}{3 ln ( 3 )} + 3) = 7

in Lambert form:

e^{u} u = \frac{21 e ^{\frac{l n ( 3 )}{4}} ln ( 3 )}{4}

Solve

e^{u} u = \frac{21 e ^{\frac{l n ( 3 )}{4}} ln ( 3 )}{4} : u = W_{0} (\frac{21 e ^{\frac{l n ( 3 )}{4}} ln ( 3 )}{4})

u = W_{0} (\frac{21 e ^{\frac{l n ( 3 )}{4}} ln ( 3 )}{4})

Substitute back

u = (3 x + \frac{9}{4}) ln (3),

solve for

x

Solve

(3 x + \frac{9}{4}) ln (3) = W_{0} (\frac{21 e ^{\frac{l n ( 3 )}{4}} ln ( 3 )}{4}) : x = \frac{4 W _{0} ( \frac{21 e ^{\frac{l n ( 3 )}{4}} l n ( 3 )}{4} ) - 9 ln ( 3 )}{12 ln ( 3 )}

x = \frac{4 W _{0} ( \frac{21 e ^{\frac{l n ( 3 )}{4}} l n ( 3 )}{4} ) - 9 ln ( 3 )}{12 ln ( 3 )}

x^{l o g_{10} (x) - 1} = 100

2^{x + 3} + 63 = \frac{8}{2 ^{x}}

3^{n} = 33

8^{\frac{7 x + 1}{x}} = 0.25

1. 1^{x} = 100

What is the answer to x4*3^{3x+2}+3^{3x+3}=7 ?
The answer to x4*3^{3x+2}+3^{3x+3}=7 is x=(4\W_{0}((21e^{\frac{ln(3))/4}ln(3))/(4))-9ln(3)}{12ln(3)}
Solve for x: x4*3^{3x+2}+3^{3x+3}=7
The solution is x=(4\W_{0}((21e^{\frac{ln(3))/4}ln(3))/(4))-9ln(3)}{12ln(3)}