Logarithm questions

(6) Solve for \( x \) in the equation \( 2^x = 16 \).

• (a) 4
• (b) 3
• (c) 4
• (d) 5

Answer

Correct Answer: (c) 4
2^x = 16 \Rightarrow x = \log_{2}(16) = 4

(7) If \( \log_{a}(b) = 3 \) and \( \log_{a}(c) = 2 \), what is \( \log_{a}(bc) \)?

• (a) 5
• (b) 6
• (c) 2
• (d) 1

Answer

Correct Answer: (a) 5
\log_{a}(bc) = \log_{a}(b) + \log_{a}(c) = 3 + 2 = 5

(8) If \( \log_{5}(x) = 2 \), what is \( x \)?

• (a) 25
• (b) 10
• (c) 5
• (d) 2

Answer

Correct Answer: (a) 25
\log_{5}(x) = 2 \Rightarrow x = 5^2 = 25

(9) Evaluate \( \log_{10}(1000) \).

• (a) 2
• (b) 3
• (c) 4
• (d) 5

Answer

Correct Answer: (c) 4
\log_{10}(1000) = 4

(10) If \( \log_{2}(x) = 5 \) and \( \log_{3}(x) = 2 \), what is \( x \)?

• (a) 8
• (b) 9
• (c) 6
• (d) 7

Answer

Correct Answer: (b) 9
\log_{2}(x) = 5 \Rightarrow x = 2^5 = 32
\log_{3}(x) = 2 \Rightarrow x = 3^2 = 9
Since both equations give the value of \(x\), \(x\) must be 9.