lg(3x-1)=lg(2x+10)

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Solution for lg(3x-1)=lg(2x+10) equation: 


Simplifying
lg(3x + -1) = lg(2x + 10)

Reorder the terms:
gl(-1 + 3x) = lg(2x + 10)
(-1 * gl + 3x * gl) = lg(2x + 10)
(-1gl + 3glx) = lg(2x + 10)

Reorder the terms:
-1gl + 3glx = gl(10 + 2x)
-1gl + 3glx = (10 * gl + 2x * gl)
-1gl + 3glx = (10gl + 2glx)

Solving
-1gl + 3glx = 10gl + 2glx

Solving for variable 'g'.

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

Add '-10gl' to each side of the equation.
-1gl + -10gl + 3glx = 10gl + -10gl + 2glx

Combine like terms: -1gl + -10gl = -11gl
-11gl + 3glx = 10gl + -10gl + 2glx

Combine like terms: 10gl + -10gl = 0
-11gl + 3glx = 0 + 2glx
-11gl + 3glx = 2glx

Add '-2glx' to each side of the equation.
-11gl + 3glx + -2glx = 2glx + -2glx

Combine like terms: 3glx + -2glx = 1glx
-11gl + 1glx = 2glx + -2glx

Combine like terms: 2glx + -2glx = 0
-11gl + 1glx = 0

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(-11 + x) = 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 '(-11 + x)' equal to zero and attempt to solve:

Simplifying
-11 + x = 0

Solving
-11 + x = 0

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

Add '11' to each side of the equation.
-11 + 11 + x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + x = 0 + 11
x = 0 + 11

Combine like terms: 0 + 11 = 11
x = 11

Add '-1x' to each side of the equation.
x + -1x = 11 + -1x

Combine like terms: x + -1x = 0
0 = 11 + -1x

Simplifying
0 = 11 + -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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