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

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

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

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

x = 3

Solution steps

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

Add

lo g_{2} (x + 1)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = 3, x = - 2

Verify Solutions:

x = 3

True

, x = - 2

False

The solution is

x = 3

x, ln (x) = ln (v) + c b

60 = 20 lo g_{10} (x)

lo g_{x + 3} (10 x + 9) = 2

lo g_{5} (x^{2} + 4 x) = 1

0.7 = lo g_{2} (\frac{X}{32000})

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