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Simplifying logb(x) + logb(x + 3) = logb(40) Multiply bglo * x bglox + logb(x + 3) = logb(40) Reorder the terms: bglox + bglo(3 + x) = logb(40) bglox + (3 * bglo + x * bglo) = logb(40) bglox + (3bglo + bglox) = logb(40) Reorder the terms: 3bglo + bglox + bglox = logb(40) Combine like terms: bglox + bglox = 2bglox 3bglo + 2bglox = logb(40) Reorder the terms for easier multiplication: 3bglo + 2bglox = 40bglo Solving 3bglo + 2bglox = 40bglo Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-40bglo' to each side of the equation. 3bglo + -40bglo + 2bglox = 40bglo + -40bglo Combine like terms: 3bglo + -40bglo = -37bglo -37bglo + 2bglox = 40bglo + -40bglo Combine like terms: 40bglo + -40bglo = 0 -37bglo + 2bglox = 0 Factor out the Greatest Common Factor (GCF), 'bglo'. bglo(-37 + 2x) = 0Subproblem 1
Set the factor 'bglo' equal to zero and attempt to solve: Simplifying bglo = 0 Solving bglo = 0 Move all terms containing b to the left, all other terms to the right. Simplifying bglo = 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 '(-37 + 2x)' equal to zero and attempt to solve: Simplifying -37 + 2x = 0 Solving -37 + 2x = 0 Move all terms containing b to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + 2x = 0 + 37 Combine like terms: -37 + 37 = 0 0 + 2x = 0 + 37 2x = 0 + 37 Combine like terms: 0 + 37 = 37 2x = 37 Add '-2x' to each side of the equation. 2x + -2x = 37 + -2x Combine like terms: 2x + -2x = 0 0 = 37 + -2x Simplifying 0 = 37 + -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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