Log[5]72-Log[5]x=3Log[5]2

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Solution for Log[5]72-Log[5]x=3Log[5]2 equation:


Simplifying
Log[5] * 72 + -1Log[5] * x = 3Log[5] * 2

Reorder the terms for easier multiplication:
5 * 72goL + -1Log[5] * x = 3Log[5] * 2

Multiply 5 * 72
360goL + -1Log[5] * x = 3Log[5] * 2

Reorder the terms for easier multiplication:
360goL + -1 * 5goL * x = 3Log[5] * 2

Multiply -1 * 5
360goL + -5goL * x = 3Log[5] * 2

Multiply goL * x
360goL + -5goxL = 3Log[5] * 2

Reorder the terms for easier multiplication:
360goL + -5goxL = 3 * 5 * 2goL

Multiply 3 * 5
360goL + -5goxL = 15 * 2goL

Multiply 15 * 2
360goL + -5goxL = 30goL

Solving
360goL + -5goxL = 30goL

Solving for variable 'g'.

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

Add '-30goL' to each side of the equation.
360goL + -30goL + -5goxL = 30goL + -30goL

Combine like terms: 360goL + -30goL = 330goL
330goL + -5goxL = 30goL + -30goL

Combine like terms: 30goL + -30goL = 0
330goL + -5goxL = 0

Factor out the Greatest Common Factor (GCF), '5goL'.
5goL(66 + -1x) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'goL' equal to zero and attempt to solve: Simplifying goL = 0 Solving goL = 0 Move all terms containing g to the left, all other terms to the right. Simplifying goL = 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 '(66 + -1x)' equal to zero and attempt to solve: Simplifying 66 + -1x = 0 Solving 66 + -1x = 0 Move all terms containing g to the left, all other terms to the right. Add '-66' to each side of the equation. 66 + -66 + -1x = 0 + -66 Combine like terms: 66 + -66 = 0 0 + -1x = 0 + -66 -1x = 0 + -66 Combine like terms: 0 + -66 = -66 -1x = -66 Add 'x' to each side of the equation. -1x + x = -66 + x Combine like terms: -1x + x = 0 0 = -66 + x Simplifying 0 = -66 + 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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