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

The answer to log_{2}(x)-log_{2}(x-2)=3 is x= 16/7

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

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

x = \frac{16}{7}

Decimal Notation

x = 2.28571 \dots

Solution steps

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

Add

lo g_{2} (x - 2)

to both sides

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

Simplify

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

Apply log rules

x = 8 (x - 2)

Solve

x = 8 (x - 2) : x = \frac{16}{7}

x = \frac{16}{7}

Verify Solutions:

x = \frac{16}{7}

True

The solution is

x = \frac{16}{7}

lo g_{2} (x + 7) = 2 - lo g_{2} (x + 4)

x, lo g_{q} (x + 20) = 2

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

0 = lo g_{3} (- x - 1)

lo g_{x} (2) = \frac{1}{3}

What is the answer to log_{2}(x)-log_{2}(x-2)=3 ?
The answer to log_{2}(x)-log_{2}(x-2)=3 is x= 16/7
Solve for x: log_{2}(x)-log_{2}(x-2)=3
The solution is x= 16/7