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

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

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log_{2}(x+1)-log_{2}(x-1)=2

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

x = \frac{5}{3}

Decimal Notation

x = 1.66666 \dots

Solution steps

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

Add

lo g_{2} (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 4 (x - 1)

Solve

x + 1 = 4 (x - 1) : x = \frac{5}{3}

x = \frac{5}{3}

Verify Solutions:

x = \frac{5}{3}

True

The solution is

x = \frac{5}{3}

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

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

lo g_{a} (5) = - 2

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

lo g_{x} (\frac{1}{6}) = - 1

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