# Quiz 1: Powers and logs¶

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## Quiz¶

This quiz tests materials in the section called “Functions, exponential and logarithm rules”. If you are struggling with the questions go back and re-read the relevant material.

**Question 1**: What is \(a^0\)?

\(0\)

\(1\)

\(a\)

None of the above

**Question 2**: What is \(3^2\)?

\(6\)

\(8\)

\(9\)

None of the above

**Question 3**: What is \(1^3\)?

\(1\)

\(3\)

\(\frac{1}{3}\)

None of the above

**Question 4**: What is \(2^{-3}\)?

\(-6\)

\(\frac{1}{8}\)

\(-9\)

None of the above

**Question 5**: What is \(\frac{4^3}{4^5}\)?

\(4^8\)

\(4^{-8}\)

\(16^{-1}\)

None of the above

**Question 6**: What is \(\left(3^{-3}\right)^3\)?

\(1\)

\(3^{-9}\)

\(3^{-27}\)

None of the above

**Question 7**: What is \(\frac{5^2}{3^2}\)?

\(\left(\frac{5}{3}\right)^2\)

\(\left(\frac{5}{3}\right)^{-2}\)

\(5^{-6}\)

None of the above

**Question 8**: What is \(4^3\)?

\(12\)

\(16\)

\(2^6\)

None of the above

**Question 9**: What is \(27^{-2/3}\)?

\(\frac{1}{18}\)

\(\frac{1}{81}\)

\(\frac{1}{9}\)

None of the above

**Question 10**: What is \(log_{10}(10^n)\)?

\(10 n\)

\(n\)

\(10^n\)

None of the above

**Question 11**: What is \(log_{10}\left(\frac{10^4}{10^{-3}}\right)\)?

\(10^7\)

\(1\)

\(10\)

\(7\)

**Question 12**: What is \(\frac{1}{2} log_{10}(16)\)?

\(4\)

\(8\)

\(log_{10}(2)\)

\(log_{10}(4)\)

**Question 13**: What is \(log_{10} [log_{10}(10)]\)?

\(10\)

\(1\)

\(0\)

\(-1\)

**Question 14**: What is \(\frac{log_{10}(1000)}{log_{10}(100)}\)?

\(\frac{3}{2}\)

\(1\)

\(-1\)

\(10\)

**Question 15**: Simplify the function

Which of these can it be written as?

\(\prod_i log(p^x_i) + \prod_i log(1 - p)^y_i\)

\(\sum_i x_i log(p) \times y_i log(1-p)\)

\(\left(\sum_i x_i\right) log(p) + \left(\sum_i y_i \right) log(1-p)\)

None of the above

**Question 16**: Simplify the function

Which of these can it be written as?

\(-n \lambda + \sum_i x_i log(\lambda) - \sum_i log(x!)\)

\(\prod_i \lambda + \prod_i log(\lambda^x_i) + \prod_i log\left(\frac{1}{x_i!}\right)\)

\(\sum_i log(-\lambda) + \sum_i x_i log(\lambda) - \sum_i log(x!)\)

None of the above