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

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

Solve for x: log_{3}(x+1)+log_{3}(3x)=1

The solution is x=(-1+sqrt(5))/2

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

x = \frac{- 1 + 5}{2}

Solution steps

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

Apply log rules

(x + 1) \cdot 3 x = 3

Solve

(x + 1) \cdot 3 x = 3 : x = \frac{- 1 + 5}{2}, x = - \frac{1 + 5}{2}

x = \frac{- 1 + 5}{2}, x = - \frac{1 + 5}{2}

Verify Solutions:

x = \frac{- 1 + 5}{2}

True

, x = - \frac{1 + 5}{2}

False

The solution is

x = \frac{- 1 + 5}{2}

lo g_{x + 5} (8) = lo g_{6} (8)

lo g_{3} (2 x + 9) - lo g_{3} (5 x) = 3

2 lo g_{2} (x) + 5 = 21

lo g_{5} (x + 7) + lo g_{5} (x - 4) = 3

∣ ln (x + 3) ∣ = 1

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