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Simplifying log5(2x) = log5(3x + -4) Remove parenthesis around (2x) g5lo * 2x = log5(3x + -4) Reorder the terms for easier multiplication: 2g5lo * x = log5(3x + -4) Multiply g5lo * x 2g5lox = log5(3x + -4) Reorder the terms: 2g5lox = g5lo(-4 + 3x) 2g5lox = (-4 * g5lo + 3x * g5lo) 2g5lox = (-4g5lo + 3g5lox) Solving 2g5lox = -4g5lo + 3g5lox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '4g5lo' to each side of the equation. 4g5lo + 2g5lox = -4g5lo + 4g5lo + 3g5lox Combine like terms: -4g5lo + 4g5lo = 0 4g5lo + 2g5lox = 0 + 3g5lox 4g5lo + 2g5lox = 3g5lox Add '-3g5lox' to each side of the equation. 4g5lo + 2g5lox + -3g5lox = 3g5lox + -3g5lox Combine like terms: 2g5lox + -3g5lox = -1g5lox 4g5lo + -1g5lox = 3g5lox + -3g5lox Combine like terms: 3g5lox + -3g5lox = 0 4g5lo + -1g5lox = 0 Factor out the Greatest Common Factor (GCF), 'g5lo'. g5lo(4 + -1x) = 0Subproblem 1
Set the factor 'g5lo' equal to zero and attempt to solve: Simplifying g5lo = 0 Solving g5lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g5lo = 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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Add 'x' to each side of the equation. -1x + x = -4 + x Combine like terms: -1x + x = 0 0 = -4 + x Simplifying 0 = -4 + x 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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