Logarithm questions

(16) If \( \log_{5}(625) = x \), what is the value of \( x \)?

• (a) 4
• (b) 3
• (c) 2
• (d) 1

Answer

Correct Answer: (a) 4
\log_{5}(625) = 4

(17) If \( \log_{6}(216) = x \), what is the value of \( x \)?

• (a) 3
• (b) 4
• (c) 2
• (d) 1

Answer

Correct Answer: (a) 3
\log_{6}(216) = 3

(18) If \( \log_{b}(a) = p \) and \( \log_{c}(a) = q \), what is \( \log_{c}(b) \)?

• (a) \(\frac{p}{q}\)
• (b) \(p + q\)
• (c) \(p – q\)
• (d) \(\frac{q}{p}\)

Answer

Correct Answer: (a) \(\frac{p}{q}\)
\log_{c}(b) = \frac{\log_{b}(b)}{\log_{b}(c)} = \frac{1}{\log_{b}(c)} = \frac{1}{q}

(19) Solve for \( x \) in the equation \( 4^x = 64 \).

• (a) 3
• (b) 4
• (c) 2
• (d) 1

Answer

Correct Answer: (a) 3
4^x = 64 \Rightarrow x = \log_{4}(64) = 3

(20) If \( \log_{2}(x) = 6 \) and \( \log_{3}(x) = 2 \), what is \( \log_{6}(x) \)?

• (a) 3
• (b) 4
• (c) 5
• (d) 6

Answer

Correct Answer: (a) 3
\log_{6}(x) = \frac{\log_{2}(x)}{\log_{2}(6)} = \frac{6}{\log_{2}(2 \cdot 3)} = \frac{6}{1} = 6