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

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

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

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

x = 4

Solution steps

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

Add

lo g_{2} (x)

to both sides

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

Simplify

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

Apply log rules

x + 4 = 2 x

Solve

x + 4 = 2 x : x = 4

x = 4

Verify Solutions:

x = 4

True

The solution is

x = 4

x^{2 \cdot l o g_{10} (x)} = 10 x^{2}

\frac{lo g _{2} ( x ) - 1}{2} = lo g_{2} (x)

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

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

lo g_{10} (2 x - 3) = 2

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