lg(5x+3)=lg(3x+2)

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Solution for lg(5x+3)=lg(3x+2) equation: 


Simplifying
lg(5x + 3) = lg(3x + 2)

Reorder the terms:
gl(3 + 5x) = lg(3x + 2)
(3 * gl + 5x * gl) = lg(3x + 2)
(3gl + 5glx) = lg(3x + 2)

Reorder the terms:
3gl + 5glx = gl(2 + 3x)
3gl + 5glx = (2 * gl + 3x * gl)
3gl + 5glx = (2gl + 3glx)

Solving
3gl + 5glx = 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.
3gl + -2gl + 5glx = 2gl + -2gl + 3glx

Combine like terms: 3gl + -2gl = 1gl
1gl + 5glx = 2gl + -2gl + 3glx

Combine like terms: 2gl + -2gl = 0
1gl + 5glx = 0 + 3glx
1gl + 5glx = 3glx

Add '-3glx' to each side of the equation.
1gl + 5glx + -3glx = 3glx + -3glx

Combine like terms: 5glx + -3glx = 2glx
1gl + 2glx = 3glx + -3glx

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

Factor out the Greatest Common Factor (GCF), 'gl'.
gl(1 + 2x) = 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 '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

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

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

Simplifying
0 = -1 + -2x

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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