What is the answer to log_{2}(1-y)-log_{2}(5+y)=3 ?

The answer to log_{2}(1-y)-log_{2}(5+y)=3 is y=-13/3

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log_{2}(1-y)-log_{2}(5+y)=3

lo g_{2} (1 - y) - lo g_{2} (5 + y) = 3

y = - \frac{13}{3}

Decimal Notation

y = - 4.33333 \dots

Solution steps

lo g_{2} (1 - y) - lo g_{2} (5 + y) = 3

Add

lo g_{2} (5 + y)

to both sides

lo g_{2} (1 - y) - lo g_{2} (5 + y) + lo g_{2} (5 + y) = 3 + lo g_{2} (5 + y)

Simplify

lo g_{2} (1 - y) = 3 + lo g_{2} (5 + y)

Apply log rules

1 - y = 8 (5 + y)

Solve

1 - y = 8 (5 + y) : y = - \frac{13}{3}

y = - \frac{13}{3}

Verify Solutions:

y = - \frac{13}{3}

True

The solution is

y = - \frac{13}{3}

lo g_{x} (3) = 2

lo g_{5} (x - 7) = 1

ln (x) - x + 2 = 0

- 2 lo g_{5} (7 x) = 2

4.7 = - lo g_{10} (x)

What is the answer to log_{2}(1-y)-log_{2}(5+y)=3 ?
The answer to log_{2}(1-y)-log_{2}(5+y)=3 is y=-13/3
Solve for y: log_{2}(1-y)-log_{2}(5+y)=3
The solution is y=-13/3