ln(5x+12)+ln(5x-12)=ln(81)

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Solution for ln(5x+12)+ln(5x-12)=ln(81) equation: 


Simplifying
ln(5x + 12) + ln(5x + -12) = ln(81)

Reorder the terms:
ln(12 + 5x) + ln(5x + -12) = ln(81)
(12 * ln + 5x * ln) + ln(5x + -12) = ln(81)
(12ln + 5lnx) + ln(5x + -12) = ln(81)

Reorder the terms:
12ln + 5lnx + ln(-12 + 5x) = ln(81)
12ln + 5lnx + (-12 * ln + 5x * ln) = ln(81)
12ln + 5lnx + (-12ln + 5lnx) = ln(81)

Reorder the terms:
12ln + -12ln + 5lnx + 5lnx = ln(81)

Combine like terms: 12ln + -12ln = 0
0 + 5lnx + 5lnx = ln(81)
5lnx + 5lnx = ln(81)

Combine like terms: 5lnx + 5lnx = 10lnx
10lnx = ln(81)

Reorder the terms for easier multiplication:
10lnx = 81ln

Solving
10lnx = 81ln

Solving for variable 'l'.

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

Add '-81ln' to each side of the equation.
-81ln + 10lnx = 81ln + -81ln

Combine like terms: 81ln + -81ln = 0
-81ln + 10lnx = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-81 + 10x) = 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 '(-81 + 10x)' equal to zero and attempt to solve:

Simplifying
-81 + 10x = 0

Solving
-81 + 10x = 0

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

Add '81' to each side of the equation.
-81 + 81 + 10x = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 10x = 0 + 81
10x = 0 + 81

Combine like terms: 0 + 81 = 81
10x = 81

Add '-10x' to each side of the equation.
10x + -10x = 81 + -10x

Combine like terms: 10x + -10x = 0
0 = 81 + -10x

Simplifying
0 = 81 + -10x

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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