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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 = -43bglo -43bglo + 2bglox = 40bglo + -40bglo Combine like terms: 40bglo + -40bglo = 0 -43bglo + 2bglox = 0 Factor out the Greatest Common Factor (GCF), 'bglo'. bglo(-43 + 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 '(-43 + 2x)' equal to zero and attempt to solve: Simplifying -43 + 2x = 0 Solving -43 + 2x = 0 Move all terms containing b to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + 2x = 0 + 43 Combine like terms: -43 + 43 = 0 0 + 2x = 0 + 43 2x = 0 + 43 Combine like terms: 0 + 43 = 43 2x = 43 Add '-2x' to each side of the equation. 2x + -2x = 43 + -2x Combine like terms: 2x + -2x = 0 0 = 43 + -2x Simplifying 0 = 43 + -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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