lg(3x-1)=lg(x+1)

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Solution for lg(3x-1)=lg(x+1) equation:


Simplifying
lg(3x + -1) = lg(x + 1)

Reorder the terms:
gl(-1 + 3x) = lg(x + 1)
(-1 * gl + 3x * gl) = lg(x + 1)
(-1gl + 3glx) = lg(x + 1)

Reorder the terms:
-1gl + 3glx = gl(1 + x)
-1gl + 3glx = (1 * gl + x * gl)
-1gl + 3glx = (1gl + glx)

Solving
-1gl + 3glx = 1gl + glx

Solving for variable 'g'.

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

Add '-1gl' to each side of the equation.
-1gl + -1gl + 3glx = 1gl + -1gl + glx

Combine like terms: -1gl + -1gl = -2gl
-2gl + 3glx = 1gl + -1gl + glx

Combine like terms: 1gl + -1gl = 0
-2gl + 3glx = 0 + glx
-2gl + 3glx = glx

Add '-1glx' to each side of the equation.
-2gl + 3glx + -1glx = glx + -1glx

Combine like terms: 3glx + -1glx = 2glx
-2gl + 2glx = glx + -1glx

Combine like terms: glx + -1glx = 0
-2gl + 2glx = 0

Factor out the Greatest Common Factor (GCF), '2gl'.
2gl(-1 + x) = 0

Ignore the factor 2.

Subproblem 1

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