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Simplifying log[5](x + 124) = 5log[5](x + 24) Reorder the terms: glo * 5(124 + x) = 5log[5](x + 24) Reorder the terms for easier multiplication: 5glo(124 + x) = 5log[5](x + 24) (124 * 5glo + x * 5glo) = 5log[5](x + 24) (620glo + 5glox) = 5log[5](x + 24) Reorder the terms: 620glo + 5glox = 5glo * 5(24 + x) Reorder the terms for easier multiplication: 620glo + 5glox = 5 * 5glo(24 + x) Multiply 5 * 5 620glo + 5glox = 25glo(24 + x) 620glo + 5glox = (24 * 25glo + x * 25glo) 620glo + 5glox = (600glo + 25glox) Solving 620glo + 5glox = 600glo + 25glox Solving for variable 'g'. Move all terms containing g to the left, all other terms to the right. Add '-600glo' to each side of the equation. 620glo + -600glo + 5glox = 600glo + -600glo + 25glox Combine like terms: 620glo + -600glo = 20glo 20glo + 5glox = 600glo + -600glo + 25glox Combine like terms: 600glo + -600glo = 0 20glo + 5glox = 0 + 25glox 20glo + 5glox = 25glox Add '-25glox' to each side of the equation. 20glo + 5glox + -25glox = 25glox + -25glox Combine like terms: 5glox + -25glox = -20glox 20glo + -20glox = 25glox + -25glox Combine like terms: 25glox + -25glox = 0 20glo + -20glox = 0 Factor out the Greatest Common Factor (GCF), '20glo'. 20glo(1 + -1x) = 0 Ignore the factor 20.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 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Add 'x' to each side of the equation. -1x + x = -1 + x Combine like terms: -1x + x = 0 0 = -1 + x Simplifying 0 = -1 + 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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