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

The answer to log_{2}(x)-log_{2}(x-1)=2 is x= 4/3

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

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

x = \frac{4}{3}

Decimal

x = 1.33333 \dots

Solution steps

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

Add

lo g_{2} (x - 1)

to both sides

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

Simplify

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

Apply log rules

x = 4 (x - 1)

Solve

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

x = \frac{4}{3}

Verify Solutions:

x = \frac{4}{3}

True

The solution is

x = \frac{4}{3}

ln (x) - 6 x^{2} ln (x) = - 5 x ln (x)

x, y^{2} + ln (x y) = 2

3 lo g_{2} (x) = 5

ln (x^{8}) - 9 ln (x) = 6

- 8 lo g_{10} (b) = - 64

What is the answer to log_{2}(x)-log_{2}(x-1)=2 ?
The answer to log_{2}(x)-log_{2}(x-1)=2 is x= 4/3
Solve for x: log_{2}(x)-log_{2}(x-1)=2
The solution is x= 4/3