What is the answer to log_{2}(x+5)=3-log_{2}(x+7) ?

The answer to log_{2}(x+5)=3-log_{2}(x+7) is x=-3

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log_{2}(x+5)=3-log_{2}(x+7)

lo g_{2} (x + 5) = 3 - lo g_{2} (x + 7)

x = - 3

Solution steps

lo g_{2} (x + 5) = 3 - lo g_{2} (x + 7)

Add

lo g_{2} (x + 7)

to both sides

lo g_{2} (x + 5) + lo g_{2} (x + 7) = 3 - lo g_{2} (x + 7) + lo g_{2} (x + 7)

Simplify

lo g_{2} (x + 5) + lo g_{2} (x + 7) = 3

Apply log rules

(x + 5) (x + 7) = 8

Solve

(x + 5) (x + 7) = 8 : x = - 3, x = - 9

x = - 3, x = - 9

Verify Solutions:

x = - 3

True

, x = - 9

False

The solution is

x = - 3

lo g_{2} (x) + lo g_{2} (- 4 x + 12) = 3

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

lo g_{5} (x) = 1

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

lo g_{10} (7 x) = 2

What is the answer to log_{2}(x+5)=3-log_{2}(x+7) ?
The answer to log_{2}(x+5)=3-log_{2}(x+7) is x=-3
Solve for x: log_{2}(x+5)=3-log_{2}(x+7)
The solution is x=-3