ln(5x+6)-lnx=8

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Solution for ln(5x+6)-lnx=8 equation:


Simplifying
ln(5x + 6) + -1lnx = 8

Reorder the terms:
ln(6 + 5x) + -1lnx = 8
(6 * ln + 5x * ln) + -1lnx = 8
(6ln + 5lnx) + -1lnx = 8

Combine like terms: 5lnx + -1lnx = 4lnx
6ln + 4lnx = 8

Solving
6ln + 4lnx = 8

Solving for variable 'l'.

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

Reorder the terms:
-8 + 6ln + 4lnx = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 6ln + 4lnx = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 3ln + 2lnx) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + 3ln + 2lnx)' equal to zero and attempt to solve: Simplifying -4 + 3ln + 2lnx = 0 Solving -4 + 3ln + 2lnx = 0 Move all terms containing l to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 3ln + 4 + 2lnx = 0 + 4 Reorder the terms: -4 + 4 + 3ln + 2lnx = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3ln + 2lnx = 0 + 4 3ln + 2lnx = 0 + 4 Combine like terms: 0 + 4 = 4 3ln + 2lnx = 4 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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