ln(3x^2-8)+ln(9)=ln(75)

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Solution for ln(3x^2-8)+ln(9)=ln(75) equation: 


Simplifying
ln(3x2 + -8) + ln(9) = ln(75)

Reorder the terms:
ln(-8 + 3x2) + ln(9) = ln(75)
(-8 * ln + 3x2 * ln) + ln(9) = ln(75)
(-8ln + 3lnx2) + ln(9) = ln(75)

Reorder the terms for easier multiplication:
-8ln + 3lnx2 + 9ln = ln(75)

Reorder the terms:
-8ln + 9ln + 3lnx2 = ln(75)

Combine like terms: -8ln + 9ln = 1ln
1ln + 3lnx2 = ln(75)

Reorder the terms for easier multiplication:
1ln + 3lnx2 = 75ln

Solving
1ln + 3lnx2 = 75ln

Solving for variable 'l'.

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

Add '-75ln' to each side of the equation.
1ln + -75ln + 3lnx2 = 75ln + -75ln

Combine like terms: 1ln + -75ln = -74ln
-74ln + 3lnx2 = 75ln + -75ln

Combine like terms: 75ln + -75ln = 0
-74ln + 3lnx2 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-74 + 3x2) = 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 '(-74 + 3x2)' equal to zero and attempt to solve:

Simplifying
-74 + 3x2 = 0

Solving
-74 + 3x2 = 0

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

Add '74' to each side of the equation.
-74 + 74 + 3x2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + 3x2 = 0 + 74
3x2 = 0 + 74

Combine like terms: 0 + 74 = 74
3x2 = 74

Add '-3x2' to each side of the equation.
3x2 + -3x2 = 74 + -3x2

Combine like terms: 3x2 + -3x2 = 0
0 = 74 + -3x2

Simplifying
0 = 74 + -3x2

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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