log(2x-5)=log(5x+4)

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Solution for log(2x-5)=log(5x+4) equation:


Simplifying
log(2x + -5) = log(5x + 4)

Reorder the terms:
glo(-5 + 2x) = log(5x + 4)
(-5 * glo + 2x * glo) = log(5x + 4)
(-5glo + 2glox) = log(5x + 4)

Reorder the terms:
-5glo + 2glox = glo(4 + 5x)
-5glo + 2glox = (4 * glo + 5x * glo)
-5glo + 2glox = (4glo + 5glox)

Solving
-5glo + 2glox = 4glo + 5glox

Solving for variable 'g'.

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

Add '-4glo' to each side of the equation.
-5glo + -4glo + 2glox = 4glo + -4glo + 5glox

Combine like terms: -5glo + -4glo = -9glo
-9glo + 2glox = 4glo + -4glo + 5glox

Combine like terms: 4glo + -4glo = 0
-9glo + 2glox = 0 + 5glox
-9glo + 2glox = 5glox

Add '-5glox' to each side of the equation.
-9glo + 2glox + -5glox = 5glox + -5glox

Combine like terms: 2glox + -5glox = -3glox
-9glo + -3glox = 5glox + -5glox

Combine like terms: 5glox + -5glox = 0
-9glo + -3glox = 0

Factor out the Greatest Common Factor (GCF), '-3glo'.
-3glo(3 + x) = 0

Ignore the factor -3.

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 '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Add '-1x' to each side of the equation. x + -1x = -3 + -1x Combine like terms: x + -1x = 0 0 = -3 + -1x Simplifying 0 = -3 + -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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