Which expressions are equivalent to the one below? check all that apply. log(10^5)

See explanation

Step-by-step explanation:

There are so many ways we can rewrite .

We can apply the power rule to obtain:

.

We could also simplify this further because

This implies that:

.

Or

.

All these are equivalent expressions.

120m^2

Step-by-step explanation:

Let's start with the bottom. Since the height, base and width are all 4m, we can say that one square = 16 m^2.

There are 5 squares (counting the bottom), and 16 * 5 = 80.

Now the top triangles. We can split the bigger triangle in half. The base is 4m, you can tell from the bottom. To find the area of the triangle, split 4 in half to find the base of the smaller triangles, which equals 2.

Now for the smaller triangles, the base is 2 and the height is 5. We know that to find a triangle's area, you do (b * h)/2, which is (2*5)/2 = 5.

The big triangle is 2 of the small triangles, so you can multiply the smaller triangle's area by 2, which is 5 * 2 = 10.

There are 4 identical triangles at the top-- so 10 * 4 = 40.

80 + 40 = 120.

Hope this helps!