Lg(3x-8)=lg(x-2)

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Solution for Lg(3x-8)=lg(x-2) equation: 


Simplifying
Lg(3x + -8) = lg(x + -2)

Reorder the terms:
gL(-8 + 3x) = lg(x + -2)
(-8 * gL + 3x * gL) = lg(x + -2)
(-8gL + 3gxL) = lg(x + -2)

Reorder the terms:
-8gL + 3gxL = gl(-2 + x)
-8gL + 3gxL = (-2 * gl + x * gl)
-8gL + 3gxL = (-2gl + glx)

Solving
-8gL + 3gxL = -2gl + glx

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.
-8gL + 2gl + 3gxL = -2gl + 2gl + glx

Combine like terms: -2gl + 2gl = 0
-8gL + 2gl + 3gxL = 0 + glx
-8gL + 2gl + 3gxL = glx

Add '-1glx' to each side of the equation.
-8gL + 2gl + -1glx + 3gxL = glx + -1glx

Combine like terms: glx + -1glx = 0
-8gL + 2gl + -1glx + 3gxL = 0

Factor out the Greatest Common Factor (GCF), 'g'.
g(-8L + 2l + -1lx + 3xL) = 0


Subproblem 1
Set the factor 'g' equal to zero and attempt to solve:

Simplifying
g = 0

Solving
g = 0

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

Simplifying
g = 0

Subproblem 2
Set the factor '(-8L + 2l + -1lx + 3xL)' equal to zero and attempt to solve:

Simplifying
-8L + 2l + -1lx + 3xL = 0

Solving
-8L + 2l + -1lx + 3xL = 0

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

Add '8L' to each side of the equation.
-8L + 2l + -1lx + 8L + 3xL = 0 + 8L

Reorder the terms:
-8L + 8L + 2l + -1lx + 3xL = 0 + 8L

Combine like terms: -8L + 8L = 0
0 + 2l + -1lx + 3xL = 0 + 8L
2l + -1lx + 3xL = 0 + 8L
Remove the zero:
2l + -1lx + 3xL = 8L

Add '-2l' to each side of the equation.
2l + -1lx + -2l + 3xL = 8L + -2l

Reorder the terms:
2l + -2l + -1lx + 3xL = 8L + -2l

Combine like terms: 2l + -2l = 0
0 + -1lx + 3xL = 8L + -2l
-1lx + 3xL = 8L + -2l

Add 'lx' to each side of the equation.
-1lx + lx + 3xL = 8L + -2l + lx

Combine like terms: -1lx + lx = 0
0 + 3xL = 8L + -2l + lx
3xL = 8L + -2l + lx

Add '-3xL' to each side of the equation.
3xL + -3xL = 8L + -2l + lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = 8L + -2l + lx + -3xL

Simplifying
0 = 8L + -2l + lx + -3xL

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
g = {0}

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