What is the answer to 2log_{10}(2-x)-log_{10}(x+5)=1 ?

The answer to 2log_{10}(2-x)-log_{10}(x+5)=1 is x=7-sqrt(95)

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2log_{10}(2-x)-log_{10}(x+5)=1

2 lo g_{10} (2 - x) - lo g_{10} (x + 5) = 1

x = 7 - 95

Decimal Notation

x = - 2.74679 \dots

Solution steps

2 lo g_{10} (2 - x) - lo g_{10} (x + 5) = 1

Apply log rules

(2 - x)^{2} = 10 (x + 5)

Solve

(2 - x)^{2} = 10 (x + 5) : x = 7 + 95, x = 7 - 95

x = 7 + 95, x = 7 - 95

Verify Solutions:

x = 7 + 95

False

, x = 7 - 95

True

The solution is

x = 7 - 95

lo g_{4} (3 x - 6) = lo g_{4} (2 - x)

lo g_{10} (2 x) = (4) + lo g_{10} (3)

lo g_{4} (x - 3) + lo g_{4} (2) = 1

lo g_{2} (x) + lo g_{2} (4) = lo g_{2} (20)

lo g_{2} (x - 5) = lo g_{4} (x - 2) + lo g_{2} (2)

What is the answer to 2log_{10}(2-x)-log_{10}(x+5)=1 ?
The answer to 2log_{10}(2-x)-log_{10}(x+5)=1 is x=7-sqrt(95)
Solve for x: 2log_{10}(2-x)-log_{10}(x+5)=1
The solution is x=7-sqrt(95)