What is the answer to 2log_{2}(x-1)-log_{2}(4-x)=2 ?

The answer to 2log_{2}(x-1)-log_{2}(4-x)=2 is x=3

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2log_{2}(x-1)-log_{2}(4-x)=2

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

x = 3

Solution steps

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

Apply log rules

(x - 1)^{2} = 4 (4 - x)

Solve

(x - 1)^{2} = 4 (4 - x) : x = 3, x = - 5

x = 3, x = - 5

Verify Solutions:

x = 3

True

, x = - 5

False

The solution is

x = 3

(lo g_{10} (x^{2}))^{2} = 1

ln (x + 2) = ln (12) - ln (x + 3)

lo g_{10} (C) = 10

lo g_{10} (x) = - lo g_{10} (ab)

lo g_{2} (\frac{x}{10000}) = 50

What is the answer to 2log_{2}(x-1)-log_{2}(4-x)=2 ?
The answer to 2log_{2}(x-1)-log_{2}(4-x)=2 is x=3
Solve for x: 2log_{2}(x-1)-log_{2}(4-x)=2
The solution is x=3