What is the answer to log_{5}(x+7)=-log_{5}(x+3)+1 ?

The answer to log_{5}(x+7)=-log_{5}(x+3)+1 is x=-2

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log_{5}(x+7)=-log_{5}(x+3)+1

lo g_{5} (x + 7) = - lo g_{5} (x + 3) + 1

x = - 2

Solution steps

lo g_{5} (x + 7) = - lo g_{5} (x + 3) + 1

Add

lo g_{5} (x + 3)

to both sides

lo g_{5} (x + 7) + lo g_{5} (x + 3) = - lo g_{5} (x + 3) + 1 + lo g_{5} (x + 3)

Simplify

lo g_{5} (x + 7) + lo g_{5} (x + 3) = 1

Apply log rules

(x + 7) (x + 3) = 5

Solve

(x + 7) (x + 3) = 5 : x = - 2, x = - 8

x = - 2, x = - 8

Verify Solutions:

x = - 2

True

, x = - 8

False

The solution is

x = - 2

lo g_{2} (x^{3}) = lo g_{8} (x)

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

lo g_{2 a} (4) = 2

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

lo g_{10} (x) \frac{1}{25} = - 2

What is the answer to log_{5}(x+7)=-log_{5}(x+3)+1 ?
The answer to log_{5}(x+7)=-log_{5}(x+3)+1 is x=-2
Solve for x: log_{5}(x+7)=-log_{5}(x+3)+1
The solution is x=-2