What is the answer to solvefor y,x=1-3ln(2-3y) ?

The answer to solvefor y,x=1-3ln(2-3y) is y=-(e^{-(x-1)/3}-2)/(3)

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solvefor y,x=1-3ln(2-3y)

solve for

y, x = 1 - 3 ln (2 - 3 y)

y = - \frac{e ^{- \frac{x - 1}{3}} - 2}{3}

Solution steps

x = 1 - 3 ln (2 - 3 y)

Switch sides

1 - 3 ln (2 - 3 y) = x

Move

1

to the right side

- 3 ln (2 - 3 y) = x - 1

Divide both sides by

- 3

ln (2 - 3 y) = - \frac{x - 1}{3}

Apply log rules

2 - 3 y = e^{- \frac{x - 1}{3}}

Solve

2 - 3 y = e^{- \frac{x - 1}{3}} : y = - \frac{e ^{- \frac{x - 1}{3}} - 2}{3}

y = - \frac{e ^{- \frac{x - 1}{3}} - 2}{3}

Verify Solutions:

y = - \frac{e ^{- \frac{x - 1}{3}} - 2}{3}

True

The solution is

y = - \frac{e ^{- \frac{x - 1}{3}} - 2}{3}

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ln (x - 2 x^{2}) + ln (4) = 0

lo g_{x^{2}} (x) = lo g_{4} (x)

What is the answer to solvefor y,x=1-3ln(2-3y) ?
The answer to solvefor y,x=1-3ln(2-3y) is y=-(e^{-(x-1)/3}-2)/(3)