What is the answer to log_{2}(2x+6)-log_{2}(x)=3 ?

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

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log_{2}(2x+6)-log_{2}(x)=3

lo g_{2} (2 x + 6) - lo g_{2} (x) = 3

x = 1

Solution steps

lo g_{2} (2 x + 6) - lo g_{2} (x) = 3

Add

lo g_{2} (x)

to both sides

lo g_{2} (2 x + 6) - lo g_{2} (x) + lo g_{2} (x) = 3 + lo g_{2} (x)

Simplify

lo g_{2} (2 x + 6) = 3 + lo g_{2} (x)

Apply log rules

2 x + 6 = 8 x

Solve

2 x + 6 = 8 x : x = 1

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

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

lo g_{10} (x + 2) + lo g_{10} (4) = 1

7 - ln (3 - x) = 0

ln (x) + x = - 1

x, ln (x^{2}) = 14

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