logb(x)+logb(x-2)=logb(24)

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Solution for logb(x)+logb(x-2)=logb(24) equation:


Simplifying
logb(x) + logb(x + -2) = logb(24)

Multiply bglo * x
bglox + logb(x + -2) = logb(24)

Reorder the terms:
bglox + bglo(-2 + x) = logb(24)
bglox + (-2 * bglo + x * bglo) = logb(24)
bglox + (-2bglo + bglox) = logb(24)

Reorder the terms:
-2bglo + bglox + bglox = logb(24)

Combine like terms: bglox + bglox = 2bglox
-2bglo + 2bglox = logb(24)

Reorder the terms for easier multiplication:
-2bglo + 2bglox = 24bglo

Solving
-2bglo + 2bglox = 24bglo

Solving for variable 'b'.

Move all terms containing b to the left, all other terms to the right.

Add '-24bglo' to each side of the equation.
-2bglo + -24bglo + 2bglox = 24bglo + -24bglo

Combine like terms: -2bglo + -24bglo = -26bglo
-26bglo + 2bglox = 24bglo + -24bglo

Combine like terms: 24bglo + -24bglo = 0
-26bglo + 2bglox = 0

Factor out the Greatest Common Factor (GCF), '2bglo'.
2bglo(-13 + x) = 0

Ignore the factor 2.

Subproblem 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 '(-13 + x)' equal to zero and attempt to solve: Simplifying -13 + x = 0 Solving -13 + x = 0 Move all terms containing b to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + x = 0 + 13 x = 0 + 13 Combine like terms: 0 + 13 = 13 x = 13 Add '-1x' to each side of the equation. x + -1x = 13 + -1x Combine like terms: x + -1x = 0 0 = 13 + -1x Simplifying 0 = 13 + -1x 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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