Ln(x-1)+ln(5x)=3

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Solution for Ln(x-1)+ln(5x)=3 equation: 


Simplifying
Ln(x + -1) + ln(5x) = 3

Reorder the terms:
nL(-1 + x) + ln(5x) = 3
(-1 * nL + x * nL) + ln(5x) = 3
(-1nL + nxL) + ln(5x) = 3

Remove parenthesis around (5x)
-1nL + nxL + ln * 5x = 3

Reorder the terms for easier multiplication:
-1nL + nxL + 5ln * x = 3

Multiply ln * x
-1nL + nxL + 5lnx = 3

Reorder the terms:
5lnx + -1nL + nxL = 3

Solving
5lnx + -1nL + nxL = 3

Solving for variable 'l'.

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

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

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

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

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

Divide each side by '5nx'.
l = 0.6n-1x-1 + 0.2x-1L + -0.2L

Simplifying
l = 0.6n-1x-1 + 0.2x-1L + -0.2L

Reorder the terms:
l = -0.2L + 0.6n-1x-1 + 0.2x-1L

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