x^2*ln(2x+1)=5*ln(2x+1)

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Solution for x^2*ln(2x+1)=5*ln(2x+1) equation:


Simplifying
x2 * ln(2x + 1) = 5ln(2x + 1)

Reorder the terms:
x2 * ln(1 + 2x) = 5ln(2x + 1)

Multiply x2 * ln
lnx2(1 + 2x) = 5ln(2x + 1)
(1 * lnx2 + 2x * lnx2) = 5ln(2x + 1)
(1lnx2 + 2lnx3) = 5ln(2x + 1)

Reorder the terms:
1lnx2 + 2lnx3 = 5ln(1 + 2x)
1lnx2 + 2lnx3 = (1 * 5ln + 2x * 5ln)
1lnx2 + 2lnx3 = (5ln + 10lnx)

Solving
1lnx2 + 2lnx3 = 5ln + 10lnx

Solving for variable 'l'.

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

Add '-5ln' to each side of the equation.
1lnx2 + -5ln + 2lnx3 = 5ln + -5ln + 10lnx

Reorder the terms:
-5ln + 1lnx2 + 2lnx3 = 5ln + -5ln + 10lnx

Combine like terms: 5ln + -5ln = 0
-5ln + 1lnx2 + 2lnx3 = 0 + 10lnx
-5ln + 1lnx2 + 2lnx3 = 10lnx

Add '-10lnx' to each side of the equation.
-5ln + 1lnx2 + -10lnx + 2lnx3 = 10lnx + -10lnx

Reorder the terms:
-5ln + -10lnx + 1lnx2 + 2lnx3 = 10lnx + -10lnx

Combine like terms: 10lnx + -10lnx = 0
-5ln + -10lnx + 1lnx2 + 2lnx3 = 0

Factor out the Greatest Common Factor (GCF), 'ln'.
ln(-5 + -10x + x2 + 2x3) = 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 '(-5 + -10x + x2 + 2x3)' equal to zero and attempt to solve: Simplifying -5 + -10x + x2 + 2x3 = 0 Solving -5 + -10x + x2 + 2x3 = 0 Move all terms containing l to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -10x + x2 + 5 + 2x3 = 0 + 5 Reorder the terms: -5 + 5 + -10x + x2 + 2x3 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -10x + x2 + 2x3 = 0 + 5 -10x + x2 + 2x3 = 0 + 5 Combine like terms: 0 + 5 = 5 -10x + x2 + 2x3 = 5 Add '10x' to each side of the equation. -10x + x2 + 10x + 2x3 = 5 + 10x Reorder the terms: -10x + 10x + x2 + 2x3 = 5 + 10x Combine like terms: -10x + 10x = 0 0 + x2 + 2x3 = 5 + 10x x2 + 2x3 = 5 + 10x Add '-1x2' to each side of the equation. x2 + -1x2 + 2x3 = 5 + 10x + -1x2 Combine like terms: x2 + -1x2 = 0 0 + 2x3 = 5 + 10x + -1x2 2x3 = 5 + 10x + -1x2 Add '-2x3' to each side of the equation. 2x3 + -2x3 = 5 + 10x + -1x2 + -2x3 Combine like terms: 2x3 + -2x3 = 0 0 = 5 + 10x + -1x2 + -2x3 Simplifying 0 = 5 + 10x + -1x2 + -2x3 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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