Log(8x)=log(3x+45)

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Solution for Log(8x)=log(3x+45) equation:


Simplifying
Log(8x) = log(3x + 45)

Remove parenthesis around (8x)
goL * 8x = log(3x + 45)

Reorder the terms for easier multiplication:
8goL * x = log(3x + 45)

Multiply goL * x
8goxL = log(3x + 45)

Reorder the terms:
8goxL = glo(45 + 3x)
8goxL = (45 * glo + 3x * glo)
8goxL = (45glo + 3glox)

Solving
8goxL = 45glo + 3glox

Solving for variable 'g'.

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

Add '-45glo' to each side of the equation.
-45glo + 8goxL = 45glo + -45glo + 3glox

Combine like terms: 45glo + -45glo = 0
-45glo + 8goxL = 0 + 3glox
-45glo + 8goxL = 3glox

Add '-3glox' to each side of the equation.
-45glo + -3glox + 8goxL = 3glox + -3glox

Combine like terms: 3glox + -3glox = 0
-45glo + -3glox + 8goxL = 0

Factor out the Greatest Common Factor (GCF), 'go'.
go(-45l + -3lx + 8xL) = 0

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 '(-45l + -3lx + 8xL)' equal to zero and attempt to solve: Simplifying -45l + -3lx + 8xL = 0 Solving -45l + -3lx + 8xL = 0 Move all terms containing g to the left, all other terms to the right. Add '45l' to each side of the equation. -45l + -3lx + 45l + 8xL = 0 + 45l Reorder the terms: -45l + 45l + -3lx + 8xL = 0 + 45l Combine like terms: -45l + 45l = 0 0 + -3lx + 8xL = 0 + 45l -3lx + 8xL = 0 + 45l Remove the zero: -3lx + 8xL = 45l Add '3lx' to each side of the equation. -3lx + 3lx + 8xL = 45l + 3lx Combine like terms: -3lx + 3lx = 0 0 + 8xL = 45l + 3lx 8xL = 45l + 3lx Add '-8xL' to each side of the equation. 8xL + -8xL = 45l + 3lx + -8xL Combine like terms: 8xL + -8xL = 0 0 = 45l + 3lx + -8xL Simplifying 0 = 45l + 3lx + -8xL 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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