loga(x-2)+loga(4x+1)=2loga(2x-3)

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Solution for loga(x-2)+loga(4x+1)=2loga(2x-3) equation:


Simplifying
loga(x + -2) + loga(4x + 1) = 2loga(2x + -3)

Reorder the terms:
aglo(-2 + x) + loga(4x + 1) = 2loga(2x + -3)
(-2 * aglo + x * aglo) + loga(4x + 1) = 2loga(2x + -3)
(-2aglo + aglox) + loga(4x + 1) = 2loga(2x + -3)

Reorder the terms:
-2aglo + aglox + aglo(1 + 4x) = 2loga(2x + -3)
-2aglo + aglox + (1 * aglo + 4x * aglo) = 2loga(2x + -3)
-2aglo + aglox + (1aglo + 4aglox) = 2loga(2x + -3)

Reorder the terms:
-2aglo + 1aglo + aglox + 4aglox = 2loga(2x + -3)

Combine like terms: -2aglo + 1aglo = -1aglo
-1aglo + aglox + 4aglox = 2loga(2x + -3)

Combine like terms: aglox + 4aglox = 5aglox
-1aglo + 5aglox = 2loga(2x + -3)

Reorder the terms:
-1aglo + 5aglox = 2aglo(-3 + 2x)
-1aglo + 5aglox = (-3 * 2aglo + 2x * 2aglo)
-1aglo + 5aglox = (-6aglo + 4aglox)

Solving
-1aglo + 5aglox = -6aglo + 4aglox

Solving for variable 'a'.

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

Add '6aglo' to each side of the equation.
-1aglo + 6aglo + 5aglox = -6aglo + 6aglo + 4aglox

Combine like terms: -1aglo + 6aglo = 5aglo
5aglo + 5aglox = -6aglo + 6aglo + 4aglox

Combine like terms: -6aglo + 6aglo = 0
5aglo + 5aglox = 0 + 4aglox
5aglo + 5aglox = 4aglox

Add '-4aglox' to each side of the equation.
5aglo + 5aglox + -4aglox = 4aglox + -4aglox

Combine like terms: 5aglox + -4aglox = 1aglox
5aglo + 1aglox = 4aglox + -4aglox

Combine like terms: 4aglox + -4aglox = 0
5aglo + 1aglox = 0

Factor out the Greatest Common Factor (GCF), 'aglo'.
aglo(5 + x) = 0

Subproblem 1

Set the factor 'aglo' equal to zero and attempt to solve: Simplifying aglo = 0 Solving aglo = 0 Move all terms containing a to the left, all other terms to the right. Simplifying aglo = 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 '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Add '-1x' to each side of the equation. x + -1x = -5 + -1x Combine like terms: x + -1x = 0 0 = -5 + -1x Simplifying 0 = -5 + -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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