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Simplifying log[3](5x + 4) = log[3](7x) Reorder the terms: glo * 3(4 + 5x) = log[3](7x) Reorder the terms for easier multiplication: 3glo(4 + 5x) = log[3](7x) (4 * 3glo + 5x * 3glo) = log[3](7x) (12glo + 15glox) = log[3](7x) Remove parenthesis around (7x) 12glo + 15glox = glo * 3 * 7x Reorder the terms for easier multiplication: 12glo + 15glox = 3 * 7glo * x Multiply 3 * 7 12glo + 15glox = 21glo * x Multiply glo * x 12glo + 15glox = 21glox Solving 12glo + 15glox = 21glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-21glox' to each side of the equation. 12glo + 15glox + -21glox = 21glox + -21glox Combine like terms: 15glox + -21glox = -6glox 12glo + -6glox = 21glox + -21glox Combine like terms: 21glox + -21glox = 0 12glo + -6glox = 0 Factor out the Greatest Common Factor (GCF), '6glo'. 6glo(2 + -1x) = 0 Ignore the factor 6.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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Add 'x' to each side of the equation. -1x + x = -2 + x Combine like terms: -1x + x = 0 0 = -2 + x Simplifying 0 = -2 + 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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