6 November, 14:29

# What is the solution to the equation below? log6 4x 2 - log6 x=2

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1. 6 November, 16:30
0
Log[6] * 4x2 + - 1log[6] * x = 2

Reorder the terms for easier multiplication:

6 * 4glo * x2 + - 1log[6] * x = 2

Multiply 6 * 4

24glo * x2 + - 1log[6] * x = 2

Multiply glo * x2

24glox2 + - 1log[6] * x = 2

Reorder the terms for easier multiplication:

24glox2 + - 1 * 6glo * x = 2

Multiply - 1 * 6

24glox2 + - 6glo * x = 2

Multiply glo * x

24glox2 + - 6glox = 2

Reorder the terms:

-6glox + 24glox2 = 2

Solving

-6glox + 24glox2 = 2

Solving for variable 'g'.

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

Reorder the terms:

-2 + - 6glox + 24glox2 = 2 + - 2

Combine like terms: 2 + - 2 = 0

-2 + - 6glox + 24glox2 = 0

Factor out the Greatest Common Factor (GCF), '2'.

2 (-1 + - 3glox + 12glox2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor ' (-1 + - 3glox + 12glox2) ' equal to zero and attempt to solve:

Simplifying

-1 + - 3glox + 12glox2 = 0

Solving

-1 + - 3glox + 12glox2 = 0

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

Add '1' to each side of the equation.

-1 + - 3glox + 1 + 12glox2 = 0 + 1

Reorder the terms:

-1 + 1 + - 3glox + 12glox2 = 0 + 1

Combine like terms: - 1 + 1 = 0

0 + - 3glox + 12glox2 = 0 + 1

-3glox + 12glox2 = 0 + 1

Combine like terms: 0 + 1 = 1

-3glox + 12glox2 = 1