Ln(x^2-25)=ln(-5x-1)

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Solution for Ln(x^2-25)=ln(-5x-1) equation: 


Simplifying
Ln(x2 + -25) = ln(-5x + -1)

Reorder the terms:
nL(-25 + x2) = ln(-5x + -1)
(-25 * nL + x2 * nL) = ln(-5x + -1)
(-25nL + nx2L) = ln(-5x + -1)

Reorder the terms:
-25nL + nx2L = ln(-1 + -5x)
-25nL + nx2L = (-1 * ln + -5x * ln)
-25nL + nx2L = (-1ln + -5lnx)

Solving
-25nL + nx2L = -1ln + -5lnx

Solving for variable 'n'.

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

Add 'ln' to each side of the equation.
-25nL + ln + nx2L = -1ln + ln + -5lnx

Reorder the terms:
ln + -25nL + nx2L = -1ln + ln + -5lnx

Combine like terms: -1ln + ln = 0
ln + -25nL + nx2L = 0 + -5lnx
ln + -25nL + nx2L = -5lnx

Add '5lnx' to each side of the equation.
ln + -25nL + 5lnx + nx2L = -5lnx + 5lnx

Reorder the terms:
ln + 5lnx + -25nL + nx2L = -5lnx + 5lnx

Combine like terms: -5lnx + 5lnx = 0
ln + 5lnx + -25nL + nx2L = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(l + 5lx + -25L + x2L) = 0


Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0

Subproblem 2
Set the factor '(l + 5lx + -25L + x2L)' equal to zero and attempt to solve:

Simplifying
l + 5lx + -25L + x2L = 0

Reorder the terms:
-25L + l + 5lx + x2L = 0

Solving
-25L + l + 5lx + x2L = 0

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

Add '25L' to each side of the equation.
-25L + l + 5lx + 25L + x2L = 0 + 25L

Reorder the terms:
-25L + 25L + l + 5lx + x2L = 0 + 25L

Combine like terms: -25L + 25L = 0
0 + l + 5lx + x2L = 0 + 25L
l + 5lx + x2L = 0 + 25L
Remove the zero:
l + 5lx + x2L = 25L

Add '-1l' to each side of the equation.
l + 5lx + -1l + x2L = 25L + -1l

Reorder the terms:
l + -1l + 5lx + x2L = 25L + -1l

Combine like terms: l + -1l = 0
0 + 5lx + x2L = 25L + -1l
5lx + x2L = 25L + -1l

Add '-5lx' to each side of the equation.
5lx + -5lx + x2L = 25L + -1l + -5lx

Combine like terms: 5lx + -5lx = 0
0 + x2L = 25L + -1l + -5lx
x2L = 25L + -1l + -5lx

Add '-1x2L' to each side of the equation.
x2L + -1x2L = 25L + -1l + -5lx + -1x2L

Combine like terms: x2L + -1x2L = 0
0 = 25L + -1l + -5lx + -1x2L

Simplifying
0 = 25L + -1l + -5lx + -1x2L

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
n = {0}

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