What is the answer to log_{2}(2x)+log_{2}(x+2)=3 ?

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

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log_{2}(2x)+log_{2}(x+2)=3

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

x = - 1 + 5

Decimal Notation

x = 1.23606 \dots

Solution steps

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

Apply log rules

2 x (x + 2) = 8

Solve

2 x (x + 2) = 8 : x = - 1 + 5, x = - 1 - 5

x = - 1 + 5, x = - 1 - 5

Verify Solutions:

x = - 1 + 5

True

, x = - 1 - 5

False

The solution is

x = - 1 + 5

7 lo g_{10} (u) = 1

ln (x^{2}) + 2 x - 5 = 0

ln (x) = 4 lo g_{x} (e)

lo g_{9} (4) = 2 lo g_{9} (x)

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

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