What is the answer to log_{2}(x+8)=2-log_{2}(x+5) ?

The answer to log_{2}(x+8)=2-log_{2}(x+5) is x=-4

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log_{2}(x+8)=2-log_{2}(x+5)

lo g_{2} (x + 8) = 2 - lo g_{2} (x + 5)

x = - 4

Solution steps

lo g_{2} (x + 8) = 2 - lo g_{2} (x + 5)

Add

lo g_{2} (x + 5)

to both sides

lo g_{2} (x + 8) + lo g_{2} (x + 5) = 2 - lo g_{2} (x + 5) + lo g_{2} (x + 5)

Simplify

lo g_{2} (x + 8) + lo g_{2} (x + 5) = 2

Apply log rules

(x + 8) (x + 5) = 4

Solve

(x + 8) (x + 5) = 4 : x = - 4, x = - 9

x = - 4, x = - 9

Verify Solutions:

x = - 4

True

, x = - 9

False

The solution is

x = - 4

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

lo g_{2} (x + 1) = 5

lo g_{x} (5) + lo g_{x} (12) = 7

\frac{ln ( x ) + 1}{2} = ln (x)

lo g_{10} (x) + lo g_{10} (x - 7) = 2

What is the answer to log_{2}(x+8)=2-log_{2}(x+5) ?
The answer to log_{2}(x+8)=2-log_{2}(x+5) is x=-4
Solve for x: log_{2}(x+8)=2-log_{2}(x+5)
The solution is x=-4