Ln(x+5)+lnx=(x+10)

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Solution for Ln(x+5)+lnx=(x+10) equation: 


Simplifying
Ln(x + 5) + lnx = (x + 10)

Reorder the terms:
nL(5 + x) + lnx = (x + 10)
(5 * nL + x * nL) + lnx = (x + 10)
(5nL + nxL) + lnx = (x + 10)

Reorder the terms:
lnx + 5nL + nxL = (x + 10)

Reorder the terms:
lnx + 5nL + nxL = (10 + x)

Remove parenthesis around (10 + x)
lnx + 5nL + nxL = 10 + x

Solving
lnx + 5nL + nxL = 10 + x

Solving for variable 'l'.

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

Add '-5nL' to each side of the equation.
lnx + 5nL + -5nL + nxL = 10 + -5nL + x

Combine like terms: 5nL + -5nL = 0
lnx + 0 + nxL = 10 + -5nL + x
lnx + nxL = 10 + -5nL + x

Add '-1nxL' to each side of the equation.
lnx + nxL + -1nxL = 10 + -5nL + -1nxL + x

Combine like terms: nxL + -1nxL = 0
lnx + 0 = 10 + -5nL + -1nxL + x
lnx = 10 + -5nL + -1nxL + x

Divide each side by 'nx'.
l = 10n-1x-1 + -5x-1L + -1L + n-1

Simplifying
l = 10n-1x-1 + -5x-1L + -1L + n-1

Reorder the terms:
l = -1L + n-1 + 10n-1x-1 + -5x-1L

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