2lgx=lg(3x-2)

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Solution for 2lgx=lg(3x-2) equation: 


Simplifying
2lgx = lg(3x + -2)

Reorder the terms:
2glx = gl(-2 + 3x)
2glx = (-2 * gl + 3x * gl)
2glx = (-2gl + 3glx)

Solving
2glx = -2gl + 3glx

Solving for variable 'g'.

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

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

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

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

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

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

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


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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Add 'x' to each side of the equation.
-1x + x = -2 + x

Combine like terms: -1x + x = 0
0 = -2 + x

Simplifying
0 = -2 + x

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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