2log[3]x+log[3]5=log[3](14x+3)

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Solution for 2log[3]x+log[3]5=log[3](14x+3) equation:


Simplifying
2log[3] * x + log[3] * 5 = log[3](14x + 3)

Reorder the terms for easier multiplication:
2 * 3glo * x + log[3] * 5 = log[3](14x + 3)

Multiply 2 * 3
6glo * x + log[3] * 5 = log[3](14x + 3)

Multiply glo * x
6glox + log[3] * 5 = log[3](14x + 3)

Reorder the terms for easier multiplication:
6glox + 3 * 5glo = log[3](14x + 3)

Multiply 3 * 5
6glox + 15glo = log[3](14x + 3)

Reorder the terms:
15glo + 6glox = log[3](14x + 3)

Reorder the terms:
15glo + 6glox = glo * 3(3 + 14x)

Reorder the terms for easier multiplication:
15glo + 6glox = 3glo(3 + 14x)
15glo + 6glox = (3 * 3glo + 14x * 3glo)
15glo + 6glox = (9glo + 42glox)

Solving
15glo + 6glox = 9glo + 42glox

Solving for variable 'g'.

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

Add '-9glo' to each side of the equation.
15glo + -9glo + 6glox = 9glo + -9glo + 42glox

Combine like terms: 15glo + -9glo = 6glo
6glo + 6glox = 9glo + -9glo + 42glox

Combine like terms: 9glo + -9glo = 0
6glo + 6glox = 0 + 42glox
6glo + 6glox = 42glox

Add '-42glox' to each side of the equation.
6glo + 6glox + -42glox = 42glox + -42glox

Combine like terms: 6glox + -42glox = -36glox
6glo + -36glox = 42glox + -42glox

Combine like terms: 42glox + -42glox = 0
6glo + -36glox = 0

Factor out the Greatest Common Factor (GCF), '6glo'.
6glo(1 + -6x) = 0

Ignore the factor 6.

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 '(1 + -6x)' equal to zero and attempt to solve: Simplifying 1 + -6x = 0 Solving 1 + -6x = 0 Move all terms containing g to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -6x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6x = 0 + -1 -6x = 0 + -1 Combine like terms: 0 + -1 = -1 -6x = -1 Add '6x' to each side of the equation. -6x + 6x = -1 + 6x Combine like terms: -6x + 6x = 0 0 = -1 + 6x Simplifying 0 = -1 + 6x 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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