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Simplifying log[14](1 + -5x) = log[14](-3x + 3) Reorder the terms for easier multiplication: 14glo(1 + -5x) = log[14](-3x + 3) (1 * 14glo + -5x * 14glo) = log[14](-3x + 3) (14glo + -70glox) = log[14](-3x + 3) Reorder the terms: 14glo + -70glox = glo * 14(3 + -3x) Reorder the terms for easier multiplication: 14glo + -70glox = 14glo(3 + -3x) 14glo + -70glox = (3 * 14glo + -3x * 14glo) 14glo + -70glox = (42glo + -42glox) Solving 14glo + -70glox = 42glo + -42glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-42glo' to each side of the equation. 14glo + -42glo + -70glox = 42glo + -42glo + -42glox Combine like terms: 14glo + -42glo = -28glo -28glo + -70glox = 42glo + -42glo + -42glox Combine like terms: 42glo + -42glo = 0 -28glo + -70glox = 0 + -42glox -28glo + -70glox = -42glox Add '42glox' to each side of the equation. -28glo + -70glox + 42glox = -42glox + 42glox Combine like terms: -70glox + 42glox = -28glox -28glo + -28glox = -42glox + 42glox Combine like terms: -42glox + 42glox = 0 -28glo + -28glox = 0 Factor out the Greatest Common Factor (GCF), '-28glo'. -28glo(1 + x) = 0 Ignore the factor -28.Subproblem 1
Set the factor 'glo' equal to zero and attempt to solve: Simplifying glo = 0 Solving glo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying glo = 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 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Add '-1x' to each side of the equation. x + -1x = -1 + -1x Combine like terms: x + -1x = 0 0 = -1 + -1x Simplifying 0 = -1 + -1x 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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