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

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

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

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

x = - 3

Solution steps

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

Add

lo g_{2} (x + 4)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = - 3, x = - 8

Verify Solutions:

x = - 3

True

, x = - 8

False

The solution is

x = - 3

x, lo g_{q} (x + 20) = 2

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

0 = lo g_{3} (- x - 1)

lo g_{x} (2) = \frac{1}{3}

lo g_{4} (- 3 x + 7) = 1

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