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

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

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

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

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

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

Add

lo g_{2} (x)

to both sides

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

Simplify

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

Apply log rules

x + 2 = 4 x

Solve

x + 2 = 4 x : x = \frac{2}{3}

x = \frac{2}{3}

Verify Solutions:

x = \frac{2}{3}

True

The solution is

x = \frac{2}{3}

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

lo g_{3} (2 x + 1) - lo g_{3} (x - 7) = 2

lo g_{4} (x + 6) + lo g_{4} (x + 18) = 3

lo g_{7} (x) = 2.5

0.47 = lo g_{10} (x)

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