Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. log4 7 -log4 m

Options:
1) log4 (m / 7)
2) log8 (7 / m)
3) log4 (7 / m)
4) log4 (7 - m)

Option 3:

Step-by-step explanation:

Logarithmic functions represented by means that where x > 0, b > 0, and b ≠ 1.

According to the quotient rule:

In the given problem, since both logs have the same base = 4, then we can model to the quotient rule, resulting in:

Quotient rule:  

Therefore, the correct answer is Option 3:

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation:

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.