log(5)log(10x)=log(3)log(x+3)

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Solution for log(5)log(10x)=log(3)log(x+3) equation:


Simplifying
log(5) * log(10x) = log(3) * log(x + 3)

Remove parenthesis around (10x)
glo * 5glo * 10x = log(3) * log(x + 3)

Reorder the terms for easier multiplication:
5 * 10glo * glo * x = log(3) * log(x + 3)

Multiply 5 * 10
50glo * glo * x = log(3) * log(x + 3)

Multiply glo * glo
50g2l2o2 * x = log(3) * log(x + 3)

Multiply g2l2o2 * x
50g2l2o2x = log(3) * log(x + 3)

Reorder the terms:
50g2l2o2x = glo * 3glo(3 + x)

Reorder the terms for easier multiplication:
50g2l2o2x = 3glo * glo(3 + x)

Multiply glo * glo
50g2l2o2x = 3g2l2o2(3 + x)
50g2l2o2x = (3 * 3g2l2o2 + x * 3g2l2o2)
50g2l2o2x = (9g2l2o2 + 3g2l2o2x)

Solving
50g2l2o2x = 9g2l2o2 + 3g2l2o2x

Solving for variable 'g'.

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

Add '-9g2l2o2' to each side of the equation.
-9g2l2o2 + 50g2l2o2x = 9g2l2o2 + -9g2l2o2 + 3g2l2o2x

Combine like terms: 9g2l2o2 + -9g2l2o2 = 0
-9g2l2o2 + 50g2l2o2x = 0 + 3g2l2o2x
-9g2l2o2 + 50g2l2o2x = 3g2l2o2x

Add '-3g2l2o2x' to each side of the equation.
-9g2l2o2 + 50g2l2o2x + -3g2l2o2x = 3g2l2o2x + -3g2l2o2x

Combine like terms: 50g2l2o2x + -3g2l2o2x = 47g2l2o2x
-9g2l2o2 + 47g2l2o2x = 3g2l2o2x + -3g2l2o2x

Combine like terms: 3g2l2o2x + -3g2l2o2x = 0
-9g2l2o2 + 47g2l2o2x = 0

Factor out the Greatest Common Factor (GCF), 'g2l2o2'.
g2l2o2(-9 + 47x) = 0

Subproblem 1

Set the factor 'g2l2o2' equal to zero and attempt to solve: Simplifying g2l2o2 = 0 Solving g2l2o2 = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g2l2o2 = 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 '(-9 + 47x)' equal to zero and attempt to solve: Simplifying -9 + 47x = 0 Solving -9 + 47x = 0 Move all terms containing g to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 47x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 47x = 0 + 9 47x = 0 + 9 Combine like terms: 0 + 9 = 9 47x = 9 Add '-47x' to each side of the equation. 47x + -47x = 9 + -47x Combine like terms: 47x + -47x = 0 0 = 9 + -47x Simplifying 0 = 9 + -47x 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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