Ln*x-1+ln*x+2=ln*6x-8

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Solution for Ln*x-1+ln*x+2=ln*6x-8 equation:


Simplifying
Ln * x + -1 + ln * x + 2 = ln * 6x + -8

Multiply nL * x
nxL + -1 + ln * x + 2 = ln * 6x + -8

Multiply ln * x
nxL + -1 + lnx + 2 = ln * 6x + -8

Reorder the terms:
-1 + 2 + lnx + nxL = ln * 6x + -8

Combine like terms: -1 + 2 = 1
1 + lnx + nxL = ln * 6x + -8

Reorder the terms for easier multiplication:
1 + lnx + nxL = 6ln * x + -8

Multiply ln * x
1 + lnx + nxL = 6lnx + -8

Reorder the terms:
1 + lnx + nxL = -8 + 6lnx

Solving
1 + lnx + nxL = -8 + 6lnx

Solving for variable 'l'.

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

Add '-6lnx' to each side of the equation.
1 + lnx + -6lnx + nxL = -8 + 6lnx + -6lnx

Combine like terms: lnx + -6lnx = -5lnx
1 + -5lnx + nxL = -8 + 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
1 + -5lnx + nxL = -8 + 0
1 + -5lnx + nxL = -8

Add '-1' to each side of the equation.
1 + -5lnx + -1 + nxL = -8 + -1

Reorder the terms:
1 + -1 + -5lnx + nxL = -8 + -1

Combine like terms: 1 + -1 = 0
0 + -5lnx + nxL = -8 + -1
-5lnx + nxL = -8 + -1

Combine like terms: -8 + -1 = -9
-5lnx + nxL = -9

Add '-1nxL' to each side of the equation.
-5lnx + nxL + -1nxL = -9 + -1nxL

Combine like terms: nxL + -1nxL = 0
-5lnx + 0 = -9 + -1nxL
-5lnx = -9 + -1nxL

Divide each side by '-5nx'.
l = 1.8n-1x-1 + 0.2L

Simplifying
l = 1.8n-1x-1 + 0.2L

Reorder the terms:
l = 0.2L + 1.8n-1x-1

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