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

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

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12