lg(6x-5)=lg(2x-1)

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Solution for lg(6x-5)=lg(2x-1) equation:


Simplifying
lg(6x + -5) = lg(2x + -1)

Reorder the terms:
gl(-5 + 6x) = lg(2x + -1)
(-5 * gl + 6x * gl) = lg(2x + -1)
(-5gl + 6glx) = lg(2x + -1)

Reorder the terms:
-5gl + 6glx = gl(-1 + 2x)
-5gl + 6glx = (-1 * gl + 2x * gl)
-5gl + 6glx = (-1gl + 2glx)

Solving
-5gl + 6glx = -1gl + 2glx

Solving for variable 'g'.

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

Add 'gl' to each side of the equation.
-5gl + gl + 6glx = -1gl + gl + 2glx

Combine like terms: -5gl + gl = -4gl
-4gl + 6glx = -1gl + gl + 2glx

Combine like terms: -1gl + gl = 0
-4gl + 6glx = 0 + 2glx
-4gl + 6glx = 2glx

Add '-2glx' to each side of the equation.
-4gl + 6glx + -2glx = 2glx + -2glx

Combine like terms: 6glx + -2glx = 4glx
-4gl + 4glx = 2glx + -2glx

Combine like terms: 2glx + -2glx = 0
-4gl + 4glx = 0

Factor out the Greatest Common Factor (GCF), '4gl'.
4gl(-1 + x) = 0

Ignore the factor 4.

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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