Daily Math · 2026-07-07

Question 1

The value of $\log_2 6 + \log_2 \dfrac{8}{3}$ is:

Accepted Answer

$\log_2 6 + \log_2 \dfrac{8}{3} = \log_2\!\left(6 \cdot \dfrac{8}{3}\right) = \log_2 16 = 4$.

Answer

$\log_2 \dfrac{8}{3}$

Answer

$\log_2 14$

Answer

$4$

Answer

$6$

Question 2

The coefficient of $x^3$ in $(x + 2)^5$ is:

Accepted Answer

$5 - k = 3 \Rightarrow k = 2$. Coefficient: $\binom{5}{2} \cdot 2^2 = 10 \cdot 4 = 40$.

Answer

$20$

Answer

$32$

Answer

$40$

Answer

$80$

Question 3

If the mean of $\{x_1, x_2, \ldots, x_n\}$ is $\bar{x}$, the mean of $\{x_1 + 5, x_2 + 5, \ldots, x_n + 5\}$ is:

Accepted Answer

$\dfrac{1}{n}\sum (x_i + 5) = \dfrac{1}{n}\sum x_i + 5 = \bar{x} + 5$.

Answer

$\bar{x}$

Answer

$\bar{x} + 5$

Answer

$5\bar{x}$

Answer

$\bar{x} + \dfrac{5}{n}$

Problems & worked solutions