What is the answer to log_{2}(x+1)-log_{2}(x)=3 ?

The answer to log_{2}(x+1)-log_{2}(x)=3 is x= 1/7

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log_{2}(x+1)-log_{2}(x)=3

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

x = \frac{1}{7}

Decimal Notation

x = 0.14285 \dots

Solution steps

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

Add

lo g_{2} (x)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 8 x

Solve

x + 1 = 8 x : x = \frac{1}{7}

x = \frac{1}{7}

Verify Solutions:

x = \frac{1}{7}

True

The solution is

x = \frac{1}{7}

ln (x + 1) = 6 - 7 x

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

ln (e - 8 x + 1 - 1) = 20, x

x, 20 = - 20 lo g_{10} (x)

2 ln (t + 2) = 0

What is the answer to log_{2}(x+1)-log_{2}(x)=3 ?
The answer to log_{2}(x+1)-log_{2}(x)=3 is x= 1/7
Solve for x: log_{2}(x+1)-log_{2}(x)=3
The solution is x= 1/7