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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
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    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
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