HA2 SEM2 practice 2

Consider a function [math]f(x)=2\log_3x+1[/math]. Which function’s domain is the same as [math]f(x)[/math]?

Consider a function [math]f(x)=\dfrac{x(x+4)(4-x)}{(x-4)(x-1)}[/math]. Which of the following statements is true?

[math]\displaystyle{\sum^{100}_{k=1}(3k^2)}[/math] is equivalent to

If [math]9=2^x+2^{-x}[/math], which of the following is true?

Consider a convex [math]n[/math]-side polygon. Its angles can make an arithmetic sequence with common difference [math]5^\circ[/math]. If the minimum angle is [math]120^\circ[/math], which of the following statements is true?

Consider a sequence [math]a_n[/math]. If [math]\displaystyle{\sum^{n}_{k=1}a_k}=2n^3+3n^2+n[/math], what is [math]a_n[/math]?

Solve the equation [math]\log(3-\sqrt{x})=\log_{100}(x-2)[/math]. If you have two or more answers, write the smallest one.

What is the minimum positive integer solution to the inequality [math]\dfrac{2x}{x-1}< x+2[/math]?

Let [math]a, b, c>1[/math] be real numbers. If the value of [math]a^{\log\frac{b}{c}}\times b^{\log\frac{c}{a}}\times c^{\log\frac{a}{b}}[/math] is always a constant, what is this constant?