Daily Math · 2026-06-11

Question 1

$\dfrac{\log_3 81}{\log_3 9}$ equals:

Accepted Answer

$\log_3 81 = 4$, $\log_3 9 = 2$, so the ratio is $	frac{4}{2} = 2$.

Answer

$2$

Answer

$	frac{1}{2}$

Answer

$9$

Answer

$3$

Question 2

If $x = \log_2 5$, then $4^x$ equals:

Accepted Answer

$4^x = 2^{2x} = (2^x)^2 = 5^2 = 25$.

Answer

$5$

Answer

$10$

Answer

$25$

Answer

$\log_2 25$

Question 3

For $I_n = \displaystyle\int_0^1 \dfrac{x^n}{1 + x} \, dx$, the sum $I_n + I_{n+1}$ equals:

Accepted Answer

$I_n + I_{n+1} = \int_0^1 \dfrac{x^n + x^{n+1}}{1 + x} \, dx = \int_0^1 x^n \, dx = \dfrac{1}{n + 1}$.

Answer

$\dfrac{1}{n + 1}$

Answer

$1$

Answer

$\dfrac{1}{n}$

Answer

$\ln 2$

Problems & worked solutions