Category Archives: Algebra

Let $a > 1$ and $x > 1$ satisfy $$\log_a(\log_a(\log_a 2) + \log_a 24 – 128) = 128$$ and $\log_a(\log_a x) = 256$. Find the remainder when $x$ is divided by $1000$. 🔑 Solution: Let $a=2^n$, we have $$log_{2^n}(\log_{2^n}(\log_{2^n}2)+\log_{2^n}24-128)=128$$ $$log_{2^n}(\log_{2^n}2)+\log_{2^n}24-128=2^{128n}$$ … Continue reading →

One day sometime before 12 noon, the snow started to fall. A snow plower started to remove snow from the streets at 12 o’clock. In the first hour, it advanced 6 miles; in the second hour, it advanced 3 miles. … Continue reading →