ln(6x-5)+In(x-1)=In(5)

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Solution for ln(6x-5)+In(x-1)=In(5) equation: 


Simplifying
ln(6x + -5) + In(x + -1) = In(5)

Reorder the terms:
ln(-5 + 6x) + In(x + -1) = In(5)
(-5 * ln + 6x * ln) + In(x + -1) = In(5)
(-5ln + 6lnx) + In(x + -1) = In(5)

Reorder the terms:
-5ln + 6lnx + nI(-1 + x) = In(5)
-5ln + 6lnx + (-1 * nI + x * nI) = In(5)
-5ln + 6lnx + (-1nI + nxI) = In(5)

Reorder the terms for easier multiplication:
-5ln + 6lnx + -1nI + nxI = 5nI

Solving
-5ln + 6lnx + -1nI + nxI = 5nI

Solving for variable 'l'.

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

Add 'nI' to each side of the equation.
-5ln + 6lnx + -1nI + nI + nxI = 5nI + nI

Combine like terms: -1nI + nI = 0
-5ln + 6lnx + 0 + nxI = 5nI + nI
-5ln + 6lnx + nxI = 5nI + nI

Combine like terms: 5nI + nI = 6nI
-5ln + 6lnx + nxI = 6nI

Add '-1nxI' to each side of the equation.
-5ln + 6lnx + nxI + -1nxI = 6nI + -1nxI

Combine like terms: nxI + -1nxI = 0
-5ln + 6lnx + 0 = 6nI + -1nxI
-5ln + 6lnx = 6nI + -1nxI

Reorder the terms:
-5ln + 6lnx + -6nI + nxI = 6nI + -6nI + -1nxI + nxI

Combine like terms: 6nI + -6nI = 0
-5ln + 6lnx + -6nI + nxI = 0 + -1nxI + nxI
-5ln + 6lnx + -6nI + nxI = -1nxI + nxI

Combine like terms: -1nxI + nxI = 0
-5ln + 6lnx + -6nI + nxI = 0

Factor out the Greatest Common Factor (GCF), 'n'.
n(-5l + 6lx + -6I + xI) = 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 '(-5l + 6lx + -6I + xI)' equal to zero and attempt to solve:

Simplifying
-5l + 6lx + -6I + xI = 0

Reorder the terms:
-6I + -5l + 6lx + xI = 0

Solving
-6I + -5l + 6lx + xI = 0

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

Add '6I' to each side of the equation.
-6I + -5l + 6lx + 6I + xI = 0 + 6I

Reorder the terms:
-6I + 6I + -5l + 6lx + xI = 0 + 6I

Combine like terms: -6I + 6I = 0
0 + -5l + 6lx + xI = 0 + 6I
-5l + 6lx + xI = 0 + 6I
Remove the zero:
-5l + 6lx + xI = 6I

Add '-1xI' to each side of the equation.
-5l + 6lx + xI + -1xI = 6I + -1xI

Combine like terms: xI + -1xI = 0
-5l + 6lx + 0 = 6I + -1xI
-5l + 6lx = 6I + -1xI

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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