14lnx-lnx^12=ln(6x+7)

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Solution for 14lnx-lnx^12=ln(6x+7) equation:


Simplifying
14lnx + -1lnx12 = ln(6x + 7)

Reorder the terms:
14lnx + -1lnx12 = ln(7 + 6x)
14lnx + -1lnx12 = (7 * ln + 6x * ln)
14lnx + -1lnx12 = (7ln + 6lnx)

Solving
14lnx + -1lnx12 = 7ln + 6lnx

Solving for variable 'l'.

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

Add '-7ln' to each side of the equation.
14lnx + -7ln + -1lnx12 = 7ln + -7ln + 6lnx

Reorder the terms:
-7ln + 14lnx + -1lnx12 = 7ln + -7ln + 6lnx

Combine like terms: 7ln + -7ln = 0
-7ln + 14lnx + -1lnx12 = 0 + 6lnx
-7ln + 14lnx + -1lnx12 = 6lnx

Add '-6lnx' to each side of the equation.
-7ln + 14lnx + -6lnx + -1lnx12 = 6lnx + -6lnx

Combine like terms: 14lnx + -6lnx = 8lnx
-7ln + 8lnx + -1lnx12 = 6lnx + -6lnx

Combine like terms: 6lnx + -6lnx = 0
-7ln + 8lnx + -1lnx12 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-7 + 8x + -1x12) = 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 '(-7 + 8x + -1x12)' equal to zero and attempt to solve: Simplifying -7 + 8x + -1x12 = 0 Solving -7 + 8x + -1x12 = 0 Move all terms containing l to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 8x + 7 + -1x12 = 0 + 7 Reorder the terms: -7 + 7 + 8x + -1x12 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 8x + -1x12 = 0 + 7 8x + -1x12 = 0 + 7 Combine like terms: 0 + 7 = 7 8x + -1x12 = 7 Add '-8x' to each side of the equation. 8x + -8x + -1x12 = 7 + -8x Combine like terms: 8x + -8x = 0 0 + -1x12 = 7 + -8x -1x12 = 7 + -8x Add 'x12' to each side of the equation. -1x12 + x12 = 7 + -8x + x12 Combine like terms: -1x12 + x12 = 0 0 = 7 + -8x + x12 Simplifying 0 = 7 + -8x + x12 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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