ln(x-5)+ln(x+2)=in(x-14)

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Solution for ln(x-5)+ln(x+2)=in(x-14) equation: 


Simplifying
ln(x + -5) + ln(x + 2) = in(x + -14)

Reorder the terms:
ln(-5 + x) + ln(x + 2) = in(x + -14)
(-5 * ln + x * ln) + ln(x + 2) = in(x + -14)
(-5ln + lnx) + ln(x + 2) = in(x + -14)

Reorder the terms:
-5ln + lnx + ln(2 + x) = in(x + -14)
-5ln + lnx + (2 * ln + x * ln) = in(x + -14)
-5ln + lnx + (2ln + lnx) = in(x + -14)

Reorder the terms:
-5ln + 2ln + lnx + lnx = in(x + -14)

Combine like terms: -5ln + 2ln = -3ln
-3ln + lnx + lnx = in(x + -14)

Combine like terms: lnx + lnx = 2lnx
-3ln + 2lnx = in(x + -14)

Reorder the terms:
-3ln + 2lnx = in(-14 + x)
-3ln + 2lnx = (-14 * in + x * in)
-3ln + 2lnx = (-14in + inx)

Solving
-3ln + 2lnx = -14in + inx

Solving for variable 'l'.

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

Reorder the terms:
14in + -1inx + -3ln + 2lnx = -14in + inx + 14in + -1inx

Reorder the terms:
14in + -1inx + -3ln + 2lnx = -14in + 14in + inx + -1inx

Combine like terms: -14in + 14in = 0
14in + -1inx + -3ln + 2lnx = 0 + inx + -1inx
14in + -1inx + -3ln + 2lnx = inx + -1inx

Combine like terms: inx + -1inx = 0
14in + -1inx + -3ln + 2lnx = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(14i + -1ix + -3l + 2lx) = 0


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

Simplifying
n = 0

Solving
n = 0

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

Add '-1n' to each side of the equation.
n + -1n = 0 + -1n
Remove the zero:
0 = -1n

Simplifying
0 = -1n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(14i + -1ix + -3l + 2lx)' equal to zero and attempt to solve:

Simplifying
14i + -1ix + -3l + 2lx = 0

Solving
14i + -1ix + -3l + 2lx = 0

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

Add '-14i' to each side of the equation.
14i + -1ix + -3l + -14i + 2lx = 0 + -14i

Reorder the terms:
14i + -14i + -1ix + -3l + 2lx = 0 + -14i

Combine like terms: 14i + -14i = 0
0 + -1ix + -3l + 2lx = 0 + -14i
-1ix + -3l + 2lx = 0 + -14i
Remove the zero:
-1ix + -3l + 2lx = -14i

Add 'ix' to each side of the equation.
-1ix + -3l + ix + 2lx = -14i + ix

Reorder the terms:
-1ix + ix + -3l + 2lx = -14i + ix

Combine like terms: -1ix + ix = 0
0 + -3l + 2lx = -14i + ix
-3l + 2lx = -14i + ix

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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