log^9(3x+14)+log^9(5)=log^9(2x)

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Solution for log^9(3x+14)+log^9(5)=log^9(2x) equation:


Simplifying
log9(3x + 14) + log9(5) = log9(2x)

Reorder the terms:
g9lo(14 + 3x) + log9(5) = log9(2x)
(14 * g9lo + 3x * g9lo) + log9(5) = log9(2x)
(14g9lo + 3g9lox) + log9(5) = log9(2x)

Reorder the terms for easier multiplication:
14g9lo + 3g9lox + 5g9lo = log9(2x)

Reorder the terms:
14g9lo + 5g9lo + 3g9lox = log9(2x)

Combine like terms: 14g9lo + 5g9lo = 19g9lo
19g9lo + 3g9lox = log9(2x)

Remove parenthesis around (2x)
19g9lo + 3g9lox = g9lo * 2x

Reorder the terms for easier multiplication:
19g9lo + 3g9lox = 2g9lo * x

Multiply g9lo * x
19g9lo + 3g9lox = 2g9lox

Solving
19g9lo + 3g9lox = 2g9lox

Solving for variable 'g'.

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

Add '-2g9lox' to each side of the equation.
19g9lo + 3g9lox + -2g9lox = 2g9lox + -2g9lox

Combine like terms: 3g9lox + -2g9lox = 1g9lox
19g9lo + 1g9lox = 2g9lox + -2g9lox

Combine like terms: 2g9lox + -2g9lox = 0
19g9lo + 1g9lox = 0

Factor out the Greatest Common Factor (GCF), 'g9lo'.
g9lo(19 + x) = 0

Subproblem 1

Set the factor 'g9lo' equal to zero and attempt to solve: Simplifying g9lo = 0 Solving g9lo = 0 Move all terms containing g to the left, all other terms to the right. Simplifying g9lo = 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 '(19 + x)' equal to zero and attempt to solve: Simplifying 19 + x = 0 Solving 19 + x = 0 Move all terms containing g to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + x = 0 + -19 x = 0 + -19 Combine like terms: 0 + -19 = -19 x = -19 Add '-1x' to each side of the equation. x + -1x = -19 + -1x Combine like terms: x + -1x = 0 0 = -19 + -1x Simplifying 0 = -19 + -1x 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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