log(x-3)=log(5x)

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Solution for log(x-3)=log(5x) equation:


Simplifying
log(x + -3) = log(5x)

Reorder the terms:
glo(-3 + x) = log(5x)
(-3 * glo + x * glo) = log(5x)
(-3glo + glox) = log(5x)

Remove parenthesis around (5x)
-3glo + glox = glo * 5x

Reorder the terms for easier multiplication:
-3glo + glox = 5glo * x

Multiply glo * x
-3glo + glox = 5glox

Solving
-3glo + glox = 5glox

Solving for variable 'g'.

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

Add '-5glox' to each side of the equation.
-3glo + glox + -5glox = 5glox + -5glox

Combine like terms: glox + -5glox = -4glox
-3glo + -4glox = 5glox + -5glox

Combine like terms: 5glox + -5glox = 0
-3glo + -4glox = 0

Factor out the Greatest Common Factor (GCF), '-1glo'.
-1glo(3 + 4x) = 0

Ignore the factor -1.

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 + 4x)' equal to zero and attempt to solve: Simplifying 3 + 4x = 0 Solving 3 + 4x = 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 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Add '-4x' to each side of the equation. 4x + -4x = -3 + -4x Combine like terms: 4x + -4x = 0 0 = -3 + -4x Simplifying 0 = -3 + -4x 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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