ln(9x^2-15)=ln(49)

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Solution for ln(9x^2-15)=ln(49) equation: 


Simplifying
ln(9x2 + -15) = ln(49)

Reorder the terms:
ln(-15 + 9x2) = ln(49)
(-15 * ln + 9x2 * ln) = ln(49)
(-15ln + 9lnx2) = ln(49)

Reorder the terms for easier multiplication:
-15ln + 9lnx2 = 49ln

Solving
-15ln + 9lnx2 = 49ln

Solving for variable 'l'.

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

Add '-49ln' to each side of the equation.
-15ln + -49ln + 9lnx2 = 49ln + -49ln

Combine like terms: -15ln + -49ln = -64ln
-64ln + 9lnx2 = 49ln + -49ln

Combine like terms: 49ln + -49ln = 0
-64ln + 9lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-64 + 9x2) = 0

Factor a difference between two squares.
ln((8 + 3x)(-8 + 3x)) = 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 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 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 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Add '-3x' to each side of the equation.
3x + -3x = -8 + -3x

Combine like terms: 3x + -3x = 0
0 = -8 + -3x

Simplifying
0 = -8 + -3x

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 '(-8 + 3x)' equal to zero and attempt to solve:

Simplifying
-8 + 3x = 0

Solving
-8 + 3x = 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 + 3x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3x = 0 + 8
3x = 0 + 8

Combine like terms: 0 + 8 = 8
3x = 8

Add '-3x' to each side of the equation.
3x + -3x = 8 + -3x

Combine like terms: 3x + -3x = 0
0 = 8 + -3x

Simplifying
0 = 8 + -3x

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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