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

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


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

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

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

Multiply glo * glo
3g2l2o2(3 + x) = log(5) * log(10x)
(3 * 3g2l2o2 + x * 3g2l2o2) = log(5) * log(10x)
(9g2l2o2 + 3g2l2o2x) = log(5) * log(10x)

Remove parenthesis around (10x)
9g2l2o2 + 3g2l2o2x = glo * 5glo * 10x

Reorder the terms for easier multiplication:
9g2l2o2 + 3g2l2o2x = 5 * 10glo * glo * x

Multiply 5 * 10
9g2l2o2 + 3g2l2o2x = 50glo * glo * x

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

Multiply g2l2o2 * x
9g2l2o2 + 3g2l2o2x = 50g2l2o2x

Solving
9g2l2o2 + 3g2l2o2x = 50g2l2o2x

Solving for variable 'g'.

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

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

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

Combine like terms: 50g2l2o2x + -50g2l2o2x = 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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