Analysis Quiz 14: Challenging Mathematics Drill Quiz

Question 1: What can you say to the sum of the following two logarithm terms?

$\log_2 (3)+\log_6 (8)$

A. Their sum is less than zero.

B. Their sum is greater than zero.

Answer:

In order to answer the question correctly, we must be super familiar with how the graph of $y=\log_{10} x$ behaves.

China IMO Contest Problem: Given $\sqrt[3]{x^5-20x}=\sqrt[5]{x^3+20x}$. Find the product of all possible values of $x$.

Given that $x\ne 0$ and $x$ is real that satisfies $\large \sqrt[3]{x^5-20x}=\sqrt[5]{x^3+20x}$. Find the product of all possible values of $x$.

Answer:

Let $\large a=\sqrt[3]{x^5-20x}=\sqrt[5]{x^3+20x}$.

Consider  $\large a=\sqrt[3]{x^5-20x}$, we have:

$\large a^3=x^5-20x---(1)$

Consider $\large a=\sqrt[5]{x^3+20x}$, we have: