lg(x-1)*lgx=lgx

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Solution for lg(x-1)*lgx=lgx equation:


Simplifying
lg(x + -1) * lgx = lgx

Reorder the terms:
gl(-1 + x) * lgx = lgx

Reorder the terms for easier multiplication:
gl * glx(-1 + x) = lgx

Multiply gl * glx
g2l2x(-1 + x) = lgx
(-1 * g2l2x + x * g2l2x) = lgx
(-1g2l2x + g2l2x2) = lgx

Solving
-1g2l2x + g2l2x2 = glx

Solving for variable 'g'.

Reorder the terms:
-1glx + -1g2l2x + g2l2x2 = glx + -1glx

Combine like terms: glx + -1glx = 0
-1glx + -1g2l2x + g2l2x2 = 0

Factor out the Greatest Common Factor (GCF), 'glx'.
glx(-1 + -1gl + glx) = 0

Subproblem 1

Set the factor 'glx' equal to zero and attempt to solve: Simplifying glx = 0 Solving glx = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glx = 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 '(-1 + -1gl + glx)' equal to zero and attempt to solve: Simplifying -1 + -1gl + glx = 0 Solving -1 + -1gl + glx = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -1gl + 1 + glx = 0 + 1 Reorder the terms: -1 + 1 + -1gl + glx = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1gl + glx = 0 + 1 -1gl + glx = 0 + 1 Combine like terms: 0 + 1 = 1 -1gl + glx = 1 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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