Log[3]5+log[3]4=log[3]x

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Solution for Log[3]5+log[3]4=log[3]x equation:


Simplifying
Log[3] * 5 + log[3] * 4 = log[3] * x

Reorder the terms for easier multiplication:
3 * 5goL + log[3] * 4 = log[3] * x

Multiply 3 * 5
15goL + log[3] * 4 = log[3] * x

Reorder the terms for easier multiplication:
15goL + 3 * 4glo = log[3] * x

Multiply 3 * 4
15goL + 12glo = log[3] * x

Reorder the terms:
12glo + 15goL = log[3] * x

Reorder the terms for easier multiplication:
12glo + 15goL = 3glo * x

Multiply glo * x
12glo + 15goL = 3glox

Solving
12glo + 15goL = 3glox

Solving for variable 'g'.

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

Add '-3glox' to each side of the equation.
12glo + -3glox + 15goL = 3glox + -3glox

Combine like terms: 3glox + -3glox = 0
12glo + -3glox + 15goL = 0

Factor out the Greatest Common Factor (GCF), '3go'.
3go(4l + -1lx + 5L) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'go' equal to zero and attempt to solve: Simplifying go = 0 Solving go = 0 Move all terms containing g to the left, all other terms to the right. Simplifying go = 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 '(4l + -1lx + 5L)' equal to zero and attempt to solve: Simplifying 4l + -1lx + 5L = 0 Reorder the terms: 5L + 4l + -1lx = 0 Solving 5L + 4l + -1lx = 0 Move all terms containing g to the left, all other terms to the right. Add '-5L' to each side of the equation. 5L + 4l + -5L + -1lx = 0 + -5L Reorder the terms: 5L + -5L + 4l + -1lx = 0 + -5L Combine like terms: 5L + -5L = 0 0 + 4l + -1lx = 0 + -5L 4l + -1lx = 0 + -5L Remove the zero: 4l + -1lx = -5L Add '-4l' to each side of the equation. 4l + -4l + -1lx = -5L + -4l Combine like terms: 4l + -4l = 0 0 + -1lx = -5L + -4l -1lx = -5L + -4l Add 'lx' to each side of the equation. -1lx + lx = -5L + -4l + lx Combine like terms: -1lx + lx = 0 0 = -5L + -4l + lx Simplifying 0 = -5L + -4l + lx 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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