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

The answer to log_{2}(x)-log_{2}(x-3)=1 is x=6

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

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

x = 6

Solution steps

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

Add

lo g_{2} (x - 3)

to both sides

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

Simplify

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

Apply log rules

x = 2 (x - 3)

Solve

x = 2 (x - 3) : x = 6

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

ln (4 x^{2} - 4 x + 1) = 0

2 ln (x) = ln (x^{2})

ln (x) = 1 - ln (x + 3)

lo g_{10} (x + 3) = lo g_{10} (2 x + 1)

lo g_{\frac{1}{4}} (3 x + 7) = - 2

What is the answer to log_{2}(x)-log_{2}(x-3)=1 ?
The answer to log_{2}(x)-log_{2}(x-3)=1 is x=6
Solve for x: log_{2}(x)-log_{2}(x-3)=1
The solution is x=6