Log(3x+1)=log(5x-2)

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Solution for Log(3x+1)=log(5x-2) equation: 


Simplifying
Log(3x + 1) = log(5x + -2)

Reorder the terms:
goL(1 + 3x) = log(5x + -2)
(1 * goL + 3x * goL) = log(5x + -2)
(1goL + 3goxL) = log(5x + -2)

Reorder the terms:
1goL + 3goxL = glo(-2 + 5x)
1goL + 3goxL = (-2 * glo + 5x * glo)
1goL + 3goxL = (-2glo + 5glox)

Solving
1goL + 3goxL = -2glo + 5glox

Solving for variable 'g'.

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

Add '2glo' to each side of the equation.
1goL + 2glo + 3goxL = -2glo + 2glo + 5glox

Reorder the terms:
2glo + 1goL + 3goxL = -2glo + 2glo + 5glox

Combine like terms: -2glo + 2glo = 0
2glo + 1goL + 3goxL = 0 + 5glox
2glo + 1goL + 3goxL = 5glox

Add '-5glox' to each side of the equation.
2glo + 1goL + -5glox + 3goxL = 5glox + -5glox

Reorder the terms:
2glo + -5glox + 1goL + 3goxL = 5glox + -5glox

Combine like terms: 5glox + -5glox = 0
2glo + -5glox + 1goL + 3goxL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(2l + -5lx + L + 3xL) = 0


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

Simplifying
go = 0

Solving
go = 0

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

Simplifying
go = 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 '(2l + -5lx + L + 3xL)' equal to zero and attempt to solve:

Simplifying
2l + -5lx + L + 3xL = 0

Reorder the terms:
L + 2l + -5lx + 3xL = 0

Solving
L + 2l + -5lx + 3xL = 0

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

Add '-1L' to each side of the equation.
L + 2l + -5lx + -1L + 3xL = 0 + -1L

Reorder the terms:
L + -1L + 2l + -5lx + 3xL = 0 + -1L

Combine like terms: L + -1L = 0
0 + 2l + -5lx + 3xL = 0 + -1L
2l + -5lx + 3xL = 0 + -1L
Remove the zero:
2l + -5lx + 3xL = -1L

Add '-2l' to each side of the equation.
2l + -5lx + -2l + 3xL = -1L + -2l

Reorder the terms:
2l + -2l + -5lx + 3xL = -1L + -2l

Combine like terms: 2l + -2l = 0
0 + -5lx + 3xL = -1L + -2l
-5lx + 3xL = -1L + -2l

Add '5lx' to each side of the equation.
-5lx + 5lx + 3xL = -1L + -2l + 5lx

Combine like terms: -5lx + 5lx = 0
0 + 3xL = -1L + -2l + 5lx
3xL = -1L + -2l + 5lx

Add '-3xL' to each side of the equation.
3xL + -3xL = -1L + -2l + 5lx + -3xL

Combine like terms: 3xL + -3xL = 0
0 = -1L + -2l + 5lx + -3xL

Simplifying
0 = -1L + -2l + 5lx + -3xL

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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