What is the answer to ln(-y+4)-ln(y+3)=ln(-3y+1) ?

The answer to ln(-y+4)-ln(y+3)=ln(-3y+1) is y=-(7+sqrt(37))/6 ,y=-(7-sqrt(37))/6

Solve for y: ln(-y+4)-ln(y+3)=ln(-3y+1)

The solution is y=-(7+sqrt(37))/6 ,y=-(7-sqrt(37))/6

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ln (- y + 4) - ln (y + 3) = ln (- 3 y + 1)

y = - \frac{7 + 37}{6}, y = - \frac{7 - 37}{6}

Decimal Notation

y = - 2.18046 \dots, y = - 0.15287 \dots

Solution steps

ln (- y + 4) - ln (y + 3) = ln (- 3 y + 1)

Add

ln (y + 3)

to both sides

ln (- y + 4) - ln (y + 3) + ln (y + 3) = ln (- 3 y + 1) + ln (y + 3)

Simplify

ln (- y + 4) = ln (- 3 y + 1) + ln (y + 3)

Apply log rules

- y + 4 = (- 3 y + 1) (y + 3)

Solve

- y + 4 = (- 3 y + 1) (y + 3) : y = - \frac{7 + 37}{6}, y = - \frac{7 - 37}{6}

y = - \frac{7 + 37}{6}, y = - \frac{7 - 37}{6}

Verify Solutions:

y = - \frac{7 + 37}{6}

True

, y = - \frac{7 - 37}{6}

True

The solutions are

y = - \frac{7 + 37}{6}, y = - \frac{7 - 37}{6}

lo g_{10} (x) 16 = - 2

lo g_{2} (2 x + 3) = 4

x, 0.47 = lo g_{10} (x)

2 lo g_{10} (4 - x) = 2 - x

ln (c x^{8}) = 8 ln (c) + 8 ln (x)

What is the answer to ln(-y+4)-ln(y+3)=ln(-3y+1) ?
The answer to ln(-y+4)-ln(y+3)=ln(-3y+1) is y=-(7+sqrt(37))/6 ,y=-(7-sqrt(37))/6
Solve for y: ln(-y+4)-ln(y+3)=ln(-3y+1)
The solution is y=-(7+sqrt(37))/6 ,y=-(7-sqrt(37))/6