What is the answer to solvefor x,ln(y-1)-ln(y)=x+ln(x) ?

The answer to solvefor x,ln(y-1)-ln(y)=x+ln(x) is x=\W((y-1)/y)

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solvefor x,ln(y-1)-ln(y)=x+ln(x)

solve for

x, ln (y - 1) - ln (y) = x + ln (x)

x = W (\frac{y - 1}{y})

Solution steps

ln (y - 1) - ln (y) = x + ln (x)

Switch sides

x + ln (x) = ln (y - 1) - ln (y)

Move

x

to the right side

ln (x) = ln (y - 1) - ln (y) - x

f (x) = g (x),

then

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

e^{l n (x)} = e^{l n (y - 1) - l n (y) - x}

Simplify

e^{l n (x)} : x

Simplify

e^{l n (y - 1) - l n (y) - x} : \frac{e ^{- x} ( y - 1 )}{y}

x = \frac{e ^{- x} ( y - 1 )}{y}

Multiply both sides by

y

x y = \frac{e ^{- x} ( y - 1 )}{y} y

Simplify

x y = e^{- x} (y - 1)

Solve

x y = e^{- x} (y - 1) : x = W (\frac{y - 1}{y})

x = W (\frac{y - 1}{y})

Verify Solutions:

x = W (\frac{y - 1}{y})

True

The solution is

x = W (\frac{y - 1}{y})

2 x + 3 = 512

1200 - 5 (3 x + 30) = 600

\frac{9}{8} = \frac{k + 6}{6}

b + 1 = - 2 \frac{1}{3}

8 = a - 2

What is the answer to solvefor x,ln(y-1)-ln(y)=x+ln(x) ?
The answer to solvefor x,ln(y-1)-ln(y)=x+ln(x) is x=\W((y-1)/y)