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

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


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

Reorder the terms:
2glo(-5 + 3x) + -3 = -1
(-5 * 2glo + 3x * 2glo) + -3 = -1
(-10glo + 6glox) + -3 = -1

Reorder the terms:
-3 + -10glo + 6glox = -1

Solving
-3 + -10glo + 6glox = -1

Solving for variable 'g'.

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

Add '3' to each side of the equation.
-3 + -10glo + 3 + 6glox = -1 + 3

Reorder the terms:
-3 + 3 + -10glo + 6glox = -1 + 3

Combine like terms: -3 + 3 = 0
0 + -10glo + 6glox = -1 + 3
-10glo + 6glox = -1 + 3

Combine like terms: -1 + 3 = 2
-10glo + 6glox = 2

Reorder the terms:
-2 + -10glo + 6glox = 2 + -2

Combine like terms: 2 + -2 = 0
-2 + -10glo + 6glox = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + -5glo + 3glox) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + -5glo + 3glox)' equal to zero and attempt to solve: Simplifying -1 + -5glo + 3glox = 0 Solving -1 + -5glo + 3glox = 0 Move all terms containing g to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -5glo + 1 + 3glox = 0 + 1 Reorder the terms: -1 + 1 + -5glo + 3glox = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -5glo + 3glox = 0 + 1 -5glo + 3glox = 0 + 1 Combine like terms: 0 + 1 = 1 -5glo + 3glox = 1 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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