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How do you solve log(3x-14)= log(2x-4) - log(x-4)

User Wellen
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1 Answer

4 votes

Answer:

Simplifying

log(2x + 4) = log(14 + -3x)

Reorder the terms:

glo(4 + 2x) = log(14 + -3x)

(4 * glo + 2x * glo) = log(14 + -3x)

(4glo + 2glox) = log(14 + -3x)

4glo + 2glox = (14 * glo + -3x * glo)

4glo + 2glox = (14glo + -3glox)

Solving

4glo + 2glox = 14glo + -3glox

Solving for variable 'g'.

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

Add '-14glo' to each side of the equation.

4glo + -14glo + 2glox = 14glo + -14glo + -3glox

Combine like terms: 4glo + -14glo = -10glo

-10glo + 2glox = 14glo + -14glo + -3glox

Combine like terms: 14glo + -14glo = 0

-10glo + 2glox = 0 + -3glox

-10glo + 2glox = -3glox

Add '3glox' to each side of the equation.

-10glo + 2glox + 3glox = -3glox + 3glox

Combine like terms: 2glox + 3glox = 5glox

-10glo + 5glox = -3glox + 3glox

Combine like terms: -3glox + 3glox = 0

-10glo + 5glox = 0

Factor out the Greatest Common Factor (GCF), '5glo'.

5glo(-2 + x) = 0

Ignore the factor 5.

Subproblem 1

Set the factor 'glo' equal to zero and attempt to solve:

Simplifying

glo = 0

Solving

glo = 0

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

Simplifying

glo = 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 '(-2 + x)' equal to zero and attempt to solve:

Simplifying

-2 + x = 0

Solving

-2 + x = 0

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

Add '2' to each side of the equation.

-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0

0 + x = 0 + 2

x = 0 + 2

Combine like terms: 0 + 2 = 2

x = 2

Add '-1x' to each side of the equation.

x + -1x = 2 + -1x

Combine like terms: x + -1x = 0

0 = 2 + -1x

Simplifying

0 = 2 + -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.

Explanation:

This is answer

User Behnam Kamrani
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