In(x)-ln(x+1)=in(x+3)-ln(x+5)

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


Simplifying
In(x) + -1ln(x + 1) = in(x + 3) + -1ln(x + 5)

Multiply nI * x
nxI + -1ln(x + 1) = in(x + 3) + -1ln(x + 5)

Reorder the terms:
nxI + -1ln(1 + x) = in(x + 3) + -1ln(x + 5)
nxI + (1 * -1ln + x * -1ln) = in(x + 3) + -1ln(x + 5)
nxI + (-1ln + -1lnx) = in(x + 3) + -1ln(x + 5)

Reorder the terms:
-1ln + -1lnx + nxI = in(x + 3) + -1ln(x + 5)

Reorder the terms:
-1ln + -1lnx + nxI = in(3 + x) + -1ln(x + 5)
-1ln + -1lnx + nxI = (3 * in + x * in) + -1ln(x + 5)
-1ln + -1lnx + nxI = (3in + inx) + -1ln(x + 5)

Reorder the terms:
-1ln + -1lnx + nxI = 3in + inx + -1ln(5 + x)
-1ln + -1lnx + nxI = 3in + inx + (5 * -1ln + x * -1ln)
-1ln + -1lnx + nxI = 3in + inx + (-5ln + -1lnx)

Add 'lnx' to each side of the equation.
-1ln + -1lnx + lnx + nxI = 3in + inx + -5ln + -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-1ln + 0 + nxI = 3in + inx + -5ln + -1lnx + lnx
-1ln + nxI = 3in + inx + -5ln + -1lnx + lnx

Combine like terms: -1lnx + lnx = 0
-1ln + nxI = 3in + inx + -5ln + 0
-1ln + nxI = 3in + inx + -5ln

Solving
-1ln + nxI = 3in + inx + -5ln

Solving for variable 'l'.

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

Add '5ln' to each side of the equation.
-1ln + 5ln + nxI = 3in + inx + -5ln + 5ln

Combine like terms: -1ln + 5ln = 4ln
4ln + nxI = 3in + inx + -5ln + 5ln

Combine like terms: -5ln + 5ln = 0
4ln + nxI = 3in + inx + 0
4ln + nxI = 3in + inx

Add '-1nxI' to each side of the equation.
4ln + nxI + -1nxI = 3in + inx + -1nxI

Combine like terms: nxI + -1nxI = 0
4ln + 0 = 3in + inx + -1nxI
4ln = 3in + inx + -1nxI

Divide each side by '4n'.
l = 0.75i + 0.25ix + -0.25xI

Simplifying
l = 0.75i + 0.25ix + -0.25xI

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