What is the answer to log_{2}(x+1)-log_{2}(x-1)=4 ?

The answer to log_{2}(x+1)-log_{2}(x-1)=4 is x= 17/15

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log_{2}(x+1)-log_{2}(x-1)=4

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

x = \frac{17}{15}

Decimal Notation

x = 1.13333 \dots

Solution steps

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

Add

lo g_{2} (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 16 (x - 1)

Solve

x + 1 = 16 (x - 1) : x = \frac{17}{15}

x = \frac{17}{15}

Verify Solutions:

x = \frac{17}{15}

True

The solution is

x = \frac{17}{15}

lo g_{2} (4 X + 5) = 8 - lo g_{2} (X + 1)

2 = lo g_{9} (x)

ln (10 - 2 x^{2}) - ln (5) = ln (2)

ln (4 x) - 4 ln (x^{3}) = ln (7)

lo g_{10} (x) - lo g_{10} (2) = 2

What is the answer to log_{2}(x+1)-log_{2}(x-1)=4 ?
The answer to log_{2}(x+1)-log_{2}(x-1)=4 is x= 17/15
Solve for x: log_{2}(x+1)-log_{2}(x-1)=4
The solution is x= 17/15