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. log base two of eight minus log base two of z. log base two of z divided by eight. log base two of eight divided by z. log base two of eight minus z. log base four of eight divided by z.

Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?

The point a is at –2 and the point b is at 7. marissa would like to divide this line segment in a 4: 3 ratio, and she would like to use the formula x = (x2 – x1) + x1. what values should she substitute into the formula? a = a + b = x1 = x2 =

Two corresponding sides of two similar triangles are 3cm and 5cm. the area of the first triangle is 12cm2. what is the area of the second triangle?