Ln(3x+1)+ln(2x+3)=ln(8x+3)

Solution for Ln(3x+1)+ln(2x+3)=ln(8x+3) equation:

Simplifying
Ln(3x + 1) + ln(2x + 3) = ln(8x + 3)

Reorder the terms:
nL(1 + 3x) + ln(2x + 3) = ln(8x + 3)
(1 * nL + 3x * nL) + ln(2x + 3) = ln(8x + 3)
(1nL + 3nxL) + ln(2x + 3) = ln(8x + 3)

Reorder the terms:
1nL + 3nxL + ln(3 + 2x) = ln(8x + 3)
1nL + 3nxL + (3 * ln + 2x * ln) = ln(8x + 3)
1nL + 3nxL + (3ln + 2lnx) = ln(8x + 3)

Reorder the terms:
3ln + 2lnx + 1nL + 3nxL = ln(8x + 3)

Reorder the terms:
3ln + 2lnx + 1nL + 3nxL = ln(3 + 8x)
3ln + 2lnx + 1nL + 3nxL = (3 * ln + 8x * ln)
3ln + 2lnx + 1nL + 3nxL = (3ln + 8lnx)

Add '-3ln' to each side of the equation.
3ln + 2lnx + 1nL + -3ln + 3nxL = 3ln + -3ln + 8lnx

Reorder the terms:
3ln + -3ln + 2lnx + 1nL + 3nxL = 3ln + -3ln + 8lnx

Combine like terms: 3ln + -3ln = 0
0 + 2lnx + 1nL + 3nxL = 3ln + -3ln + 8lnx
2lnx + 1nL + 3nxL = 3ln + -3ln + 8lnx

Combine like terms: 3ln + -3ln = 0
2lnx + 1nL + 3nxL = 0 + 8lnx
2lnx + 1nL + 3nxL = 8lnx

Solving
2lnx + 1nL + 3nxL = 8lnx

Solving for variable 'l'.

Move all terms containing l to the left, all other terms to the right.

Add '-8lnx' to each side of the equation.
2lnx + 1nL + -8lnx + 3nxL = 8lnx + -8lnx

Reorder the terms:
2lnx + -8lnx + 1nL + 3nxL = 8lnx + -8lnx

Combine like terms: 2lnx + -8lnx = -6lnx
-6lnx + 1nL + 3nxL = 8lnx + -8lnx

Combine like terms: 8lnx + -8lnx = 0
-6lnx + 1nL + 3nxL = 0

Add '-1nL' to each side of the equation.
-6lnx + 1nL + -1nL + 3nxL = 0 + -1nL

Combine like terms: 1nL + -1nL = 0
-6lnx + 0 + 3nxL = 0 + -1nL
-6lnx + 3nxL = 0 + -1nL
Remove the zero:
-6lnx + 3nxL = -1nL

Add '-3nxL' to each side of the equation.
-6lnx + 3nxL + -3nxL = -1nL + -3nxL

Combine like terms: 3nxL + -3nxL = 0
-6lnx + 0 = -1nL + -3nxL
-6lnx = -1nL + -3nxL

Divide each side by '-6nx'.
l = 0.1666666667x-1L + 0.5L

Simplifying
l = 0.1666666667x-1L + 0.5L

Reorder the terms:
l = 0.5L + 0.1666666667x-1L