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

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

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

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

x = - 2

Solution steps

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

Add

lo g_{2} (x + 6)

to both sides

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

Simplify

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

Apply log rules

(x + 3) (x + 6) = 4

Solve

(x + 3) (x + 6) = 4 : x = - 2, x = - 7

x = - 2, x = - 7

Verify Solutions:

x = - 2

True

, x = - 7

False

The solution is

x = - 2

4 + 3 lo g_{10} (2 x) = 16

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

ln (x) - 1 = ln (5 + x) - 4

a, lo g_{a} (b) = c

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

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