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

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

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

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

x = 3

Solution steps

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

Add

lo g_{2} (x - 2)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 4 (x - 2)

Solve

x + 1 = 4 (x - 2) : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

2.73 = - lo g_{10} (x)

lo g_{10} (4 x + 8) - lo g_{10} (3) = 2

y, x = 2 y + ln (y)

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

8.5 = - lo g_{10} (x)

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