What is the answer to ln(3x)=ln(4x+1)+ln(1-x) ?

The answer to ln(3x)=ln(4x+1)+ln(1-x) is x= 1/2

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ln(3x)=ln(4x+1)+ln(1-x)

ln (3 x) = ln (4 x + 1) + ln (1 - x)

x = \frac{1}{2}

Decimal Notation

x = 0.5

Solution steps

ln (3 x) = ln (4 x + 1) + ln (1 - x)

Apply log rules

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

Solve

3 x = (4 x + 1) (1 - x) : x = \frac{1}{2}, x = - \frac{1}{2}

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

Verify Solutions:

x = \frac{1}{2}

True

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

False

The solution is

x = \frac{1}{2}

2 \cdot ln (x - 4) - ln (4 x) = 0

4 ln (x) = 2 ln (25)

lo g_{10} (k) = 27

lo g_{10} (x) = - 11

m, lo g_{m} (4) = d

What is the answer to ln(3x)=ln(4x+1)+ln(1-x) ?
The answer to ln(3x)=ln(4x+1)+ln(1-x) is x= 1/2
Solve for x: ln(3x)=ln(4x+1)+ln(1-x)
The solution is x= 1/2