What is the answer to 2log_{2}(x)=3+log_{2}(x+1) ?

The answer to 2log_{2}(x)=3+log_{2}(x+1) is x=2(2+sqrt(6))

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2log_{2}(x)=3+log_{2}(x+1)

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

x = 2 (2 + 6)

Decimal Notation

x = 8.89897 \dots

Solution steps

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

Apply log rules

x^{2} = 8 (x + 1)

Solve

x^{2} = 8 (x + 1) : x = 2 (2 + 6), x = 2 (2 - 6)

x = 2 (2 + 6), x = 2 (2 - 6)

Verify Solutions:

x = 2 (2 + 6)

True

, x = 2 (2 - 6)

False

The solution is

x = 2 (2 + 6)

lo g_{x} (\frac{1}{81}) = - 4

y, x = lo g_{2} (y)

2 x ln (x) - x = 0

8 x^{2} = 64 x \cdot lo g_{2} (x)

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

What is the answer to 2log_{2}(x)=3+log_{2}(x+1) ?
The answer to 2log_{2}(x)=3+log_{2}(x+1) is x=2(2+sqrt(6))
Solve for x: 2log_{2}(x)=3+log_{2}(x+1)
The solution is x=2(2+sqrt(6))