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

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

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

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

x = 6

Solution steps

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

Add

lo g_{2} (x - 4)

to both sides

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

Simplify

lo g_{2} (x + 2) - 4 + lo g_{2} (x - 4) = 0

Apply log rules

(x + 2) (x - 4) = 16

Solve

(x + 2) (x - 4) = 16 : x = 6, x = - 4

x = 6, x = - 4

Verify Solutions:

x = 6

True

, x = - 4

False

The solution is

x = 6

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

lo g_{8} (4 x) = 3

lo g_{10} (x) (\frac{1}{16}) = - 4

x, ln (x y) = c

ln (x) + ln (3 x) = 14

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