What is the answer to log_{2}(2x+4)-log_{2}(x-4)=3 ?

The answer to log_{2}(2x+4)-log_{2}(x-4)=3 is x=6

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log_{2}(2x+4)-log_{2}(x-4)=3

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

x = 6

Solution steps

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

Add

lo g_{2} (x - 4)

to both sides

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

Simplify

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

Apply log rules

2 x + 4 = 8 (x - 4)

Solve

2 x + 4 = 8 (x - 4) : x = 6

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

lo g_{3} (m + 4) - 3 = - 4

lo g_{2} (x^{2}) = 0

lo g_{2} (x) - 5 lo g_{10} (x) = 84

lo g_{2} (a) = 5

lo g_{10} (y) = 3

What is the answer to log_{2}(2x+4)-log_{2}(x-4)=3 ?
The answer to log_{2}(2x+4)-log_{2}(x-4)=3 is x=6
Solve for x: log_{2}(2x+4)-log_{2}(x-4)=3
The solution is x=6