log[4](2x-10)-log[4](3x-15)=0

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Solution for log[4](2x-10)-log[4](3x-15)=0 equation:


Simplifying
log[4](2x + -10) + -1log[4](3x + -15) = 0

Reorder the terms:
glo * 4(-10 + 2x) + -1log[4](3x + -15) = 0

Reorder the terms for easier multiplication:
4glo(-10 + 2x) + -1log[4](3x + -15) = 0
(-10 * 4glo + 2x * 4glo) + -1log[4](3x + -15) = 0
(-40glo + 8glox) + -1log[4](3x + -15) = 0

Reorder the terms:
-40glo + 8glox + -1glo * 4(-15 + 3x) = 0

Reorder the terms for easier multiplication:
-40glo + 8glox + -1 * 4glo(-15 + 3x) = 0

Multiply -1 * 4
-40glo + 8glox + -4glo(-15 + 3x) = 0
-40glo + 8glox + (-15 * -4glo + 3x * -4glo) = 0
-40glo + 8glox + (60glo + -12glox) = 0

Reorder the terms:
-40glo + 60glo + 8glox + -12glox = 0

Combine like terms: -40glo + 60glo = 20glo
20glo + 8glox + -12glox = 0

Combine like terms: 8glox + -12glox = -4glox
20glo + -4glox = 0

Solving
20glo + -4glox = 0

Solving for variable 'g'.

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

Factor out the Greatest Common Factor (GCF), '4glo'.
4glo(5 + -1x) = 0

Ignore the factor 4.

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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Add 'x' to each side of the equation. -1x + x = -5 + x Combine like terms: -1x + x = 0 0 = -5 + x Simplifying 0 = -5 + x 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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