ln(9x+1)=ln(x^2+9)

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Solution for ln(9x+1)=ln(x^2+9) equation: 


Simplifying
ln(9x + 1) = ln(x2 + 9)

Reorder the terms:
ln(1 + 9x) = ln(x2 + 9)
(1 * ln + 9x * ln) = ln(x2 + 9)
(1ln + 9lnx) = ln(x2 + 9)

Reorder the terms:
1ln + 9lnx = ln(9 + x2)
1ln + 9lnx = (9 * ln + x2 * ln)
1ln + 9lnx = (9ln + lnx2)

Solving
1ln + 9lnx = 9ln + lnx2

Solving for variable 'l'.

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

Add '-9ln' to each side of the equation.
1ln + -9ln + 9lnx = 9ln + -9ln + lnx2

Combine like terms: 1ln + -9ln = -8ln
-8ln + 9lnx = 9ln + -9ln + lnx2

Combine like terms: 9ln + -9ln = 0
-8ln + 9lnx = 0 + lnx2
-8ln + 9lnx = lnx2

Add '-1lnx2' to each side of the equation.
-8ln + 9lnx + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
-8ln + 9lnx + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-8 + 9x + -1x2) = 0

Factor a trinomial.
ln((-8 + x)(1 + -1x)) = 0


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

Simplifying
ln = 0

Solving
ln = 0

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

Simplifying
ln = 0

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 '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Add '-1x' to each side of the equation.
x + -1x = 8 + -1x

Combine like terms: x + -1x = 0
0 = 8 + -1x

Simplifying
0 = 8 + -1x

The solution to this equation could not be determined.

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

Subproblem 3
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Add 'x' to each side of the equation.
-1x + x = -1 + x

Combine like terms: -1x + x = 0
0 = -1 + x

Simplifying
0 = -1 + x

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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