Log(x+5)=Log(4x+2)

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Solution for Log(x+5)=Log(4x+2) equation:


Simplifying
Log(x + 5) = Log(4x + 2)

Reorder the terms:
goL(5 + x) = Log(4x + 2)
(5 * goL + x * goL) = Log(4x + 2)
(5goL + goxL) = Log(4x + 2)

Reorder the terms:
5goL + goxL = goL(2 + 4x)
5goL + goxL = (2 * goL + 4x * goL)
5goL + goxL = (2goL + 4goxL)

Solving
5goL + goxL = 2goL + 4goxL

Solving for variable 'g'.

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

Add '-2goL' to each side of the equation.
5goL + -2goL + goxL = 2goL + -2goL + 4goxL

Combine like terms: 5goL + -2goL = 3goL
3goL + goxL = 2goL + -2goL + 4goxL

Combine like terms: 2goL + -2goL = 0
3goL + goxL = 0 + 4goxL
3goL + goxL = 4goxL

Add '-4goxL' to each side of the equation.
3goL + goxL + -4goxL = 4goxL + -4goxL

Combine like terms: goxL + -4goxL = -3goxL
3goL + -3goxL = 4goxL + -4goxL

Combine like terms: 4goxL + -4goxL = 0
3goL + -3goxL = 0

Factor out the Greatest Common Factor (GCF), '3goL'.
3goL(1 + -1x) = 0

Ignore the factor 3.

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