ln(6t+5)=ln(7t-8)

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Solution for ln(6t+5)=ln(7t-8) equation: 


Simplifying
ln(6t + 5) = ln(7t + -8)

Reorder the terms:
ln(5 + 6t) = ln(7t + -8)
(5 * ln + 6t * ln) = ln(7t + -8)
(5ln + 6lnt) = ln(7t + -8)

Reorder the terms:
5ln + 6lnt = ln(-8 + 7t)
5ln + 6lnt = (-8 * ln + 7t * ln)
5ln + 6lnt = (-8ln + 7lnt)

Solving
5ln + 6lnt = -8ln + 7lnt

Solving for variable 'l'.

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

Add '8ln' to each side of the equation.
5ln + 8ln + 6lnt = -8ln + 8ln + 7lnt

Combine like terms: 5ln + 8ln = 13ln
13ln + 6lnt = -8ln + 8ln + 7lnt

Combine like terms: -8ln + 8ln = 0
13ln + 6lnt = 0 + 7lnt
13ln + 6lnt = 7lnt

Add '-7lnt' to each side of the equation.
13ln + 6lnt + -7lnt = 7lnt + -7lnt

Combine like terms: 6lnt + -7lnt = -1lnt
13ln + -1lnt = 7lnt + -7lnt

Combine like terms: 7lnt + -7lnt = 0
13ln + -1lnt = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(13 + -1t) = 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 '(13 + -1t)' equal to zero and attempt to solve:

Simplifying
13 + -1t = 0

Solving
13 + -1t = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1t = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1t = 0 + -13
-1t = 0 + -13

Combine like terms: 0 + -13 = -13
-1t = -13

Add 't' to each side of the equation.
-1t + t = -13 + t

Combine like terms: -1t + t = 0
0 = -13 + t

Simplifying
0 = -13 + t

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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