24. The truth set of [tex]3^{x-7} \times 3^x = 27[/tex] is:
- a) 4
- b) 5
- c) 2

25. The truth set of [tex]4(5^x) = 5^{2x} - 5[/tex] is:
- a) [tex]\(\{-1\}\)[/tex]
- b) [tex]\(\{0, 1\}\)[/tex]

26. Which of the following is not true?
- a) If [tex]\(a \ \textgreater \ 1, f(x) = a^x\)[/tex] is an increasing function.
- b) If [tex]\(a \ \textless \ 1, f(x) = a^x\)[/tex] is a decreasing function.
- c) If [tex]\(0 \ \textless \ a \ \textless \ 1\)[/tex], then [tex]\(a^x \ \textless \ 1\)[/tex] for [tex]\(x \ \textless \ 0\)[/tex].
- d) For [tex]\(a \ \textgreater \ b \ \textgreater \ 1\)[/tex], if [tex]\(a^x = b^x\)[/tex], then [tex]\(x = 0\)[/tex].

27. If [tex]\(\frac{5^x}{25^{x-1}} = 125^x\)[/tex], then what is the value of [tex]\(x\)[/tex]?
- a) [tex]\(\frac{1}{2}\)[/tex]
- b) [tex]\(\frac{1}{4}\)[/tex]
- c) [tex]\(\frac{-1}{4}\)[/tex]
- d) [tex]\(-\frac{1}{2}\)[/tex]

28. What is the factor of [tex]\(x^5 - x^4 - 6x^3\)[/tex]?
- a) [tex]\(x^2(x^2 - x - 6)\)[/tex]
- b) [tex]\(x^3(x^2 + x - 6)\)[/tex]
- c) [tex]\(x^3(x + 2)(x - 3)\)[/tex]
- d) [tex]\(x^3(x + 2)(x + 3)\)[/tex]

29. If [tex]\(\log_3(x^2 - 54) = 3\)[/tex], then [tex]\(x\)[/tex] is equal to:
- a) 9
- b) -9
- c) a and b
- d) 2

Part III: Answer the following questions with the necessary steps.

1. Find the exact value of
[tex]\[
(\log_4 3)(\log_5 4)(\log_6 5)(\log_7 6)(\log_8 7)(\log_9 8)
\][/tex]
(2 points)

2. Solve each of the following:
- a) [tex]\(4^{2x} = 8^{3x + 1}\)[/tex]
- b) [tex]\(4^x \left(\frac{1}{2}\right)^{3 - 2x} = 8 \cdot (2^x)^2\)[/tex]
- c) [tex]\(3^{x - 1} \times 3^{1 - x} = 3\)[/tex]