What is the answer to log_{2}(x+4)=-log_{2}(x+7)+2 ?

The answer to log_{2}(x+4)=-log_{2}(x+7)+2 is x=-3

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log_{2}(x+4)=-log_{2}(x+7)+2

lo g_{2} (x + 4) = - lo g_{2} (x + 7) + 2

x = - 3

Solution steps

lo g_{2} (x + 4) = - lo g_{2} (x + 7) + 2

Add

lo g_{2} (x + 7)

to both sides

lo g_{2} (x + 4) + lo g_{2} (x + 7) = - lo g_{2} (x + 7) + 2 + lo g_{2} (x + 7)

Simplify

lo g_{2} (x + 4) + lo g_{2} (x + 7) = 2

Apply log rules

(x + 4) (x + 7) = 4

Solve

(x + 4) (x + 7) = 4 : x = - 3, x = - 8

x = - 3, x = - 8

Verify Solutions:

x = - 3

True

, x = - 8

False

The solution is

x = - 3

ln (3 x - 17) = 4

2 ln (\frac{2}{x}) = e

lo g_{x - 2} (2 x^{2} - 11 x + 16) = 2

lo g_{10} (0.5 x) = - 6

lo g_{6} (\frac{x + 4}{x - 1}) = 1

What is the answer to log_{2}(x+4)=-log_{2}(x+7)+2 ?
The answer to log_{2}(x+4)=-log_{2}(x+7)+2 is x=-3
Solve for x: log_{2}(x+4)=-log_{2}(x+7)+2
The solution is x=-3