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

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


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

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

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

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

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

Combine like terms: 6glo + 15glo = 21glo
21glo = log[3](14x + 3)

Reorder the terms:
21glo = glo * 3(3 + 14x)

Reorder the terms for easier multiplication:
21glo = 3glo(3 + 14x)
21glo = (3 * 3glo + 14x * 3glo)
21glo = (9glo + 42glox)

Solving
21glo = 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.
21glo + -9glo = 9glo + -9glo + 42glox

Combine like terms: 21glo + -9glo = 12glo
12glo = 9glo + -9glo + 42glox

Combine like terms: 9glo + -9glo = 0
12glo = 0 + 42glox
12glo = 42glox

Add '-42glox' to each side of the equation.
12glo + -42glox = 42glox + -42glox

Combine like terms: 42glox + -42glox = 0
12glo + -42glox = 0

Factor out the Greatest Common Factor (GCF), '6glo'.
6glo(2 + -7x) = 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 '(2 + -7x)' equal to zero and attempt to solve: Simplifying 2 + -7x = 0 Solving 2 + -7x = 0 Move all terms containing g to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -7x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7x = 0 + -2 -7x = 0 + -2 Combine like terms: 0 + -2 = -2 -7x = -2 Add '7x' to each side of the equation. -7x + 7x = -2 + 7x Combine like terms: -7x + 7x = 0 0 = -2 + 7x Simplifying 0 = -2 + 7x 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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