6*ln(x)-ln(x^4)=ln(9x+10)

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Solution for 6*ln(x)-ln(x^4)=ln(9x+10) equation:


Simplifying
6ln(x) + -1ln(x4) = ln(9x + 10)

Multiply ln * x
6lnx + -1ln(x4) = ln(9x + 10)

Multiply ln * x4
6lnx + -1lnx4 = ln(9x + 10)

Reorder the terms:
6lnx + -1lnx4 = ln(10 + 9x)
6lnx + -1lnx4 = (10 * ln + 9x * ln)
6lnx + -1lnx4 = (10ln + 9lnx)

Solving
6lnx + -1lnx4 = 10ln + 9lnx

Solving for variable 'l'.

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

Add '-10ln' to each side of the equation.
6lnx + -10ln + -1lnx4 = 10ln + -10ln + 9lnx

Reorder the terms:
-10ln + 6lnx + -1lnx4 = 10ln + -10ln + 9lnx

Combine like terms: 10ln + -10ln = 0
-10ln + 6lnx + -1lnx4 = 0 + 9lnx
-10ln + 6lnx + -1lnx4 = 9lnx

Add '-9lnx' to each side of the equation.
-10ln + 6lnx + -9lnx + -1lnx4 = 9lnx + -9lnx

Combine like terms: 6lnx + -9lnx = -3lnx
-10ln + -3lnx + -1lnx4 = 9lnx + -9lnx

Combine like terms: 9lnx + -9lnx = 0
-10ln + -3lnx + -1lnx4 = 0

Factor out the Greatest Common Factor (GCF), '-1ln'.
-1ln(10 + 3x + x4) = 0

Ignore the factor -1.

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 '(10 + 3x + x4)' equal to zero and attempt to solve: Simplifying 10 + 3x + x4 = 0 Solving 10 + 3x + x4 = 0 Move all terms containing l to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + 3x + -10 + x4 = 0 + -10 Reorder the terms: 10 + -10 + 3x + x4 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 3x + x4 = 0 + -10 3x + x4 = 0 + -10 Combine like terms: 0 + -10 = -10 3x + x4 = -10 Add '-3x' to each side of the equation. 3x + -3x + x4 = -10 + -3x Combine like terms: 3x + -3x = 0 0 + x4 = -10 + -3x x4 = -10 + -3x Add '-1x4' to each side of the equation. x4 + -1x4 = -10 + -3x + -1x4 Combine like terms: x4 + -1x4 = 0 0 = -10 + -3x + -1x4 Simplifying 0 = -10 + -3x + -1x4 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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