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Simplifying log13(4x) = log13(2x + -3) Remove parenthesis around (4x) g13lo * 4x = log13(2x + -3) Reorder the terms for easier multiplication: 4g13lo * x = log13(2x + -3) Multiply g13lo * x 4g13lox = log13(2x + -3) Reorder the terms: 4g13lox = g13lo(-3 + 2x) 4g13lox = (-3 * g13lo + 2x * g13lo) 4g13lox = (-3g13lo + 2g13lox) Solving 4g13lox = -3g13lo + 2g13lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '3g13lo' to each side of the equation. 3g13lo + 4g13lox = -3g13lo + 3g13lo + 2g13lox Combine like terms: -3g13lo + 3g13lo = 0 3g13lo + 4g13lox = 0 + 2g13lox 3g13lo + 4g13lox = 2g13lox Add '-2g13lox' to each side of the equation. 3g13lo + 4g13lox + -2g13lox = 2g13lox + -2g13lox Combine like terms: 4g13lox + -2g13lox = 2g13lox 3g13lo + 2g13lox = 2g13lox + -2g13lox Combine like terms: 2g13lox + -2g13lox = 0 3g13lo + 2g13lox = 0 Factor out the Greatest Common Factor (GCF), 'g13lo'. g13lo(3 + 2x) = 0Subproblem 1
Set the factor 'g13lo' equal to zero and attempt to solve: Simplifying g13lo = 0 Solving g13lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g13lo = 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 '(3 + 2x)' equal to zero and attempt to solve: Simplifying 3 + 2x = 0 Solving 3 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x = 0 + -3 2x = 0 + -3 Combine like terms: 0 + -3 = -3 2x = -3 Add '-2x' to each side of the equation. 2x + -2x = -3 + -2x Combine like terms: 2x + -2x = 0 0 = -3 + -2x Simplifying 0 = -3 + -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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