Ln(x-8)+ln(x+1)=ln(x-24)

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Solution for Ln(x-8)+ln(x+1)=ln(x-24) equation: 


Simplifying
Ln(x + -8) + ln(x + 1) = ln(x + -24)

Reorder the terms:
nL(-8 + x) + ln(x + 1) = ln(x + -24)
(-8 * nL + x * nL) + ln(x + 1) = ln(x + -24)
(-8nL + nxL) + ln(x + 1) = ln(x + -24)

Reorder the terms:
-8nL + nxL + ln(1 + x) = ln(x + -24)
-8nL + nxL + (1 * ln + x * ln) = ln(x + -24)
-8nL + nxL + (1ln + lnx) = ln(x + -24)

Reorder the terms:
1ln + lnx + -8nL + nxL = ln(x + -24)

Reorder the terms:
1ln + lnx + -8nL + nxL = ln(-24 + x)
1ln + lnx + -8nL + nxL = (-24 * ln + x * ln)
1ln + lnx + -8nL + nxL = (-24ln + lnx)

Add '-1lnx' to each side of the equation.
1ln + lnx + -8nL + -1lnx + nxL = -24ln + lnx + -1lnx

Reorder the terms:
1ln + lnx + -1lnx + -8nL + nxL = -24ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
1ln + 0 + -8nL + nxL = -24ln + lnx + -1lnx
1ln + -8nL + nxL = -24ln + lnx + -1lnx

Combine like terms: lnx + -1lnx = 0
1ln + -8nL + nxL = -24ln + 0
1ln + -8nL + nxL = -24ln

Solving
1ln + -8nL + nxL = -24ln

Solving for variable 'l'.

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

Add '24ln' to each side of the equation.
1ln + -8nL + 24ln + nxL = -24ln + 24ln

Reorder the terms:
1ln + 24ln + -8nL + nxL = -24ln + 24ln

Combine like terms: 1ln + 24ln = 25ln
25ln + -8nL + nxL = -24ln + 24ln

Combine like terms: -24ln + 24ln = 0
25ln + -8nL + nxL = 0

Add '8nL' to each side of the equation.
25ln + -8nL + 8nL + nxL = 0 + 8nL

Combine like terms: -8nL + 8nL = 0
25ln + 0 + nxL = 0 + 8nL
25ln + nxL = 0 + 8nL
Remove the zero:
25ln + nxL = 8nL

Add '-1nxL' to each side of the equation.
25ln + nxL + -1nxL = 8nL + -1nxL

Combine like terms: nxL + -1nxL = 0
25ln + 0 = 8nL + -1nxL
25ln = 8nL + -1nxL

Divide each side by '25n'.
l = 0.32L + -0.04xL

Simplifying
l = 0.32L + -0.04xL

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