log(5)(3x)=log(5)(2x+7)

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Solution for log(5)(3x)=log(5)(2x+7) equation:


Simplifying
log(5)(3x) = log(5)(2x + 7)

Remove parenthesis around (3x)
glo * 5 * 3x = log(5)(2x + 7)

Reorder the terms for easier multiplication:
5 * 3glo * x = log(5)(2x + 7)

Multiply 5 * 3
15glo * x = log(5)(2x + 7)

Multiply glo * x
15glox = log(5)(2x + 7)

Reorder the terms:
15glox = glo * 5(7 + 2x)

Reorder the terms for easier multiplication:
15glox = 5glo(7 + 2x)
15glox = (7 * 5glo + 2x * 5glo)
15glox = (35glo + 10glox)

Solving
15glox = 35glo + 10glox

Solving for variable 'g'.

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

Add '-35glo' to each side of the equation.
-35glo + 15glox = 35glo + -35glo + 10glox

Combine like terms: 35glo + -35glo = 0
-35glo + 15glox = 0 + 10glox
-35glo + 15glox = 10glox

Add '-10glox' to each side of the equation.
-35glo + 15glox + -10glox = 10glox + -10glox

Combine like terms: 15glox + -10glox = 5glox
-35glo + 5glox = 10glox + -10glox

Combine like terms: 10glox + -10glox = 0
-35glo + 5glox = 0

Factor out the Greatest Common Factor (GCF), '5glo'.
5glo(-7 + x) = 0

Ignore the factor 5.

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 '(-7 + x)' equal to zero and attempt to solve: Simplifying -7 + x = 0 Solving -7 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + x = 0 + 7 x = 0 + 7 Combine like terms: 0 + 7 = 7 x = 7 Add '-1x' to each side of the equation. x + -1x = 7 + -1x Combine like terms: x + -1x = 0 0 = 7 + -1x Simplifying 0 = 7 + -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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