Try the following ACT math practice question that tests your understanding of logarithmic operations.

If $3 = k\cdot 2^r$ and $15 = k\cdot 4^r$, then $r =$

1. $\quad -\log_{2}5$
2. $\quad \log_{5}2$
3. $\quad \log_{10}5$
4. $\quad \log_{2}5$
5. $\quad \dfrac{5}{2}$

Try the following ACT math practice question that tests your understanding of principles of counting when applied to the number of handshakes at a gathering.

A total of $28$ handshakes was exchanged at the conclusion of a gathering. Assuming that each participant shook hands with every other participant, the number of people present was:

1. $\quad 56$
2. $\quad 28$
3. $\quad 14$
4. $\quad 8$
5. $\quad 7$

Try the following ACT math practice question that tests your understanding of reflection of straight lines in the coordinate plane.

Let $y=mx+b$ be the image when the line $x-3y+11=0$ is reflected across the $x$-axis. The value of $m+b$ is

1. $\quad -6$
2. $\quad -5$
3. $\quad -4$
4. $\quad -3$
5. $\quad -2$

Try the following ACT math practice question that tests your understanding of exponents and finding the number of solutions of an equation.

Let $n$ be the number of integer values of $x$ such that the below equation is true.
$$ 4^{3x-2} = 8^{2x-1} $$
Then $n$ is:

1. $\quad 0$
2. $\quad 1$
3. $\quad 2$
4. $\quad 3$
5. $\quad \textrm{Infinite}$