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

The answer to log_{2}(x+2)-log_{2}(x-2)=2 is x= 10/3

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

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

x = \frac{10}{3}

Decimal Notation

x = 3.33333 \dots

Solution steps

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

Add

lo g_{2} (x - 2)

to both sides

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

Simplify

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

Apply log rules

x + 2 = 4 (x - 2)

Solve

x + 2 = 4 (x - 2) : x = \frac{10}{3}

x = \frac{10}{3}

Verify Solutions:

x = \frac{10}{3}

True

The solution is

x = \frac{10}{3}

lo g_{3} (x + 7) = 3

1.034 + 1.4758 = 1.0445 ln (x)

lo g_{2} (3 x - 2) - lo g_{2} (x - 1) = 4

∣ lo g_{2} (x) ∣ = 3

lo g_{2} (x^{2} - 9) = 4

What is the answer to log_{2}(x+2)-log_{2}(x-2)=2 ?
The answer to log_{2}(x+2)-log_{2}(x-2)=2 is x= 10/3
Solve for x: log_{2}(x+2)-log_{2}(x-2)=2
The solution is x= 10/3