ln(9x)=ln((x^2)+14)

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Solution for ln(9x)=ln((x^2)+14) equation: 


Simplifying
ln(9x) = ln((x2) + 14)

Remove parenthesis around (9x)
ln * 9x = ln((x2) + 14)

Reorder the terms for easier multiplication:
9ln * x = ln((x2) + 14)

Multiply ln * x
9lnx = ln((x2) + 14)
9lnx = ln(x2 + 14)

Reorder the terms:
9lnx = ln(14 + x2)
9lnx = (14 * ln + x2 * ln)
9lnx = (14ln + lnx2)

Solving
9lnx = 14ln + lnx2

Solving for variable 'l'.

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

Add '-14ln' to each side of the equation.
-14ln + 9lnx = 14ln + -14ln + lnx2

Combine like terms: 14ln + -14ln = 0
-14ln + 9lnx = 0 + lnx2
-14ln + 9lnx = lnx2

Add '-1lnx2' to each side of the equation.
-14ln + 9lnx + -1lnx2 = lnx2 + -1lnx2

Combine like terms: lnx2 + -1lnx2 = 0
-14ln + 9lnx + -1lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-14 + 9x + -1x2) = 0

Factor a trinomial.
ln((-7 + x)(2 + -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 '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 0

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

Add '7' to each side of the equation.
-7 + 7 + x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + x = 0 + 7
x = 0 + 7

Combine like terms: 0 + 7 = 7
x = 7

Add '-1x' to each side of the equation.
x + -1x = 7 + -1x

Combine like terms: x + -1x = 0
0 = 7 + -1x

Simplifying
0 = 7 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Add 'x' to each side of the equation.
-1x + x = -2 + x

Combine like terms: -1x + x = 0
0 = -2 + x

Simplifying
0 = -2 + 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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