What is the answer to solvefor x,xy+ln(x)+2ln(y)=7 ?

The answer to solvefor x,xy+ln(x)+2ln(y)=7 is x=(\W((e^7)/y))/(y)

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solvefor x,xy+ln(x)+2ln(y)=7

solve for

x, x y + ln (x) + 2 ln (y) = 7

x = \frac{W ( \frac{e ^{7}}{y} )}{y}

Solution steps

x y + ln (x) + 2 ln (y) = 7

Move

x y

to the right side

ln (x) + 2 ln (y) = 7 - x y

Move

2 ln (y)

to the right side

ln (x) = 7 - x y - 2 ln (y)

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (x)} = e^{7 - x y - 2 l n (y)}

Simplify

e^{l n (x)} : x

Simplify

e^{7 - x y - 2 l n (y)} : \frac{e ^{7 - x y}}{y ^{2}}

x = \frac{e ^{7 - x y}}{y ^{2}}

Multiply both sides by

y^{2}

x y^{2} = \frac{e ^{7 - x y}}{y ^{2}} y^{2}

Simplify

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

Solve

x y^{2} = e^{7 - x y} : x = \frac{W ( \frac{e ^{7}}{y} )}{y}

x = \frac{W ( \frac{e ^{7}}{y} )}{y}

Verify Solutions:

x = \frac{W ( \frac{e ^{7}}{y} )}{y}

True

The solution is

x = \frac{W ( \frac{e ^{7}}{y} )}{y}

1 + 2 lo g_{4} (x) = lo g_{2} (x + 16)

30 = 10 \cdot lo g_{10} (x)

ln (2 x - 5) = 2

ln (2 x + 1) = 3

ln (x - 6) + 2 ln (x) = ln (x - 30)

What is the answer to solvefor x,xy+ln(x)+2ln(y)=7 ?
The answer to solvefor x,xy+ln(x)+2ln(y)=7 is x=(\W((e^7)/y))/(y)