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

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

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

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

x = \frac{7}{3}

Decimal Notation

x = 2.33333 \dots

Solution steps

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

Add

lo g_{2} (3 - x)

to both sides

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

Simplify

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

Apply log rules

5 - x = 4 (3 - x)

Solve

5 - x = 4 (3 - x) : x = \frac{7}{3}

x = \frac{7}{3}

Verify Solutions:

x = \frac{7}{3}

True

The solution is

x = \frac{7}{3}

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

lo g_{8} (x) = 1.5

lo g_{3} (5) + lo g_{3} (8 + 3 x) = 5

lo g_{2 x - 1} (256) = 8

lo g_{5} (x + 6) - lo g_{5} (x - 2) = 1

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