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

The answer to log_{2}(x+3)-log_{2}(x-5)=3 is x= 43/7

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log_{2}(x+3)-log_{2}(x-5)=3

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

x = \frac{43}{7}

Decimal Notation

x = 6.14285 \dots

Solution steps

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

Add

lo g_{2} (x - 5)

to both sides

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

Simplify

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

Apply log rules

x + 3 = 8 (x - 5)

Solve

x + 3 = 8 (x - 5) : x = \frac{43}{7}

x = \frac{43}{7}

Verify Solutions:

x = \frac{43}{7}

True

The solution is

x = \frac{43}{7}

2 \cdot lo g_{3} (x) - lo g_{3} (x + 6) + 1 = 2

lo g_{2} (x) = 0

lo g_{2} (x) = 2

lo g_{2} (x) = 6

lo g_{10} (16 - x^{2}) - lo g_{10} (3 x - 4) = 2

What is the answer to log_{2}(x+3)-log_{2}(x-5)=3 ?
The answer to log_{2}(x+3)-log_{2}(x-5)=3 is x= 43/7
Solve for x: log_{2}(x+3)-log_{2}(x-5)=3
The solution is x= 43/7