Ln(x-3)+ln(4x)=5

Solution for Ln(x-3)+ln(4x)=5 equation:

Simplifying
Ln(x + -3) + ln(4x) = 5

Reorder the terms:
nL(-3 + x) + ln(4x) = 5
(-3 * nL + x * nL) + ln(4x) = 5
(-3nL + nxL) + ln(4x) = 5

Remove parenthesis around (4x)
-3nL + nxL + ln * 4x = 5

Reorder the terms for easier multiplication:
-3nL + nxL + 4ln * x = 5

Multiply ln * x
-3nL + nxL + 4lnx = 5

Reorder the terms:
4lnx + -3nL + nxL = 5

Solving
4lnx + -3nL + nxL = 5

Solving for variable 'l'.

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

Add '3nL' to each side of the equation.
4lnx + -3nL + 3nL + nxL = 5 + 3nL

Combine like terms: -3nL + 3nL = 0
4lnx + 0 + nxL = 5 + 3nL
4lnx + nxL = 5 + 3nL

Add '-1nxL' to each side of the equation.
4lnx + nxL + -1nxL = 5 + 3nL + -1nxL

Combine like terms: nxL + -1nxL = 0
4lnx + 0 = 5 + 3nL + -1nxL
4lnx = 5 + 3nL + -1nxL

Divide each side by '4nx'.
l = 1.25n-1x-1 + 0.75x-1L + -0.25L

Simplifying
l = 1.25n-1x-1 + 0.75x-1L + -0.25L

Reorder the terms:
l = -0.25L + 1.25n-1x-1 + 0.75x-1L