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

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

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log_{2}(x+4)=3-log_{2}(x+6)

lo g_{2} (x + 4) = 3 - lo g_{2} (x + 6)

x = - 2

Solution steps

lo g_{2} (x + 4) = 3 - lo g_{2} (x + 6)

Add

lo g_{2} (x + 6)

to both sides

lo g_{2} (x + 4) + lo g_{2} (x + 6) = 3 - lo g_{2} (x + 6) + lo g_{2} (x + 6)

Simplify

lo g_{2} (x + 4) + lo g_{2} (x + 6) = 3

Apply log rules

(x + 4) (x + 6) = 8

Solve

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

x = - 2, x = - 8

Verify Solutions:

x = - 2

True

, x = - 8

False

The solution is

x = - 2

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

2 ln (x) = ln (9) + 4

p, ln (p) = r t + c

lo g_{4} (x - 5) = 1 - lo g_{4} (x - 2)

lo g_{x} (100) = 2

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