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Simplifying log(5)(2x + 3) = log(5) * 11 + log(5) * 3 Reorder the terms: glo * 5(3 + 2x) = log(5) * 11 + log(5) * 3 Reorder the terms for easier multiplication: 5glo(3 + 2x) = log(5) * 11 + log(5) * 3 (3 * 5glo + 2x * 5glo) = log(5) * 11 + log(5) * 3 (15glo + 10glox) = log(5) * 11 + log(5) * 3 Reorder the terms for easier multiplication: 15glo + 10glox = 5 * 11glo + log(5) * 3 Multiply 5 * 11 15glo + 10glox = 55glo + log(5) * 3 Reorder the terms for easier multiplication: 15glo + 10glox = 55glo + 5 * 3glo Multiply 5 * 3 15glo + 10glox = 55glo + 15glo Combine like terms: 55glo + 15glo = 70glo 15glo + 10glox = 70glo Solving 15glo + 10glox = 70glo Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-70glo' to each side of the equation. 15glo + -70glo + 10glox = 70glo + -70glo Combine like terms: 15glo + -70glo = -55glo -55glo + 10glox = 70glo + -70glo Combine like terms: 70glo + -70glo = 0 -55glo + 10glox = 0 Factor out the Greatest Common Factor (GCF), '5glo'. 5glo(-11 + 2x) = 0 Ignore the factor 5.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 '(-11 + 2x)' equal to zero and attempt to solve: Simplifying -11 + 2x = 0 Solving -11 + 2x = 0 Move all terms containing g to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + 2x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 2x = 0 + 11 2x = 0 + 11 Combine like terms: 0 + 11 = 11 2x = 11 Add '-2x' to each side of the equation. 2x + -2x = 11 + -2x Combine like terms: 2x + -2x = 0 0 = 11 + -2x Simplifying 0 = 11 + -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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