Quiz on Logarithms: Test Your Algebra 2 Knowledge

📚 Quick Study Guide

• 🔑 Definition: Logarithms are the inverse operation to exponentiation. The logarithm of a number $x$ with respect to base $b$ is the exponent to which $b$ must be raised to produce $x$. This is written as $\log_b(x) = y$, which means $b^y = x$.
• ➕ Product Rule: $\log_b(MN) = \log_b(M) + \log_b(N)$
• ➗ Quotient Rule: $\log_b(\frac{M}{N}) = \log_b(M) - \log_b(N)$
• 💪 Power Rule: $\log_b(M^k) = k \cdot \log_b(M)$
• 🔄 Change of Base Formula: $\log_b(a) = \frac{\log_c(a)}{\log_c(b)}$
• 📈 Common Logarithm: A logarithm with base 10, denoted as $\log(x)$ or $\log_{10}(x)$.
• 🌿 Natural Logarithm: A logarithm with base $e$ (Euler's number, approximately 2.718), denoted as $\ln(x)$ or $\log_e(x)$.

🧪 Practice Quiz

1. What is the value of $\log_2(8)$?
   1. 1
   2. 2
   3. 3
   4. 4
2. Simplify: $\log_3(27) - \log_3(3)$
   1. 0
   2. 1
   3. 2
   4. 3
3. Solve for $x$: $\log_5(x) = 2$
   1. 5
   2. 10
   3. 25
   4. 32
4. Which of the following is equivalent to $\log(1000)$?
   1. 1
   2. 2
   3. 3
   4. 4
5. Expand the expression: $\log_2(4x)$
   1. $\log_2(4) + \log_2(x)$
   2. $\log_2(4) - \log_2(x)$
   3. $4 \log_2(x)$
   4. $\log_2(4x)$
6. Condense the expression: $2\log(x) + \log(y)$
   1. $\log(x^2y)$
   2. $\log(x^2 + y)$
   3. $\log(2xy)$
   4. $\log((x+y)^2)$
7. Evaluate: $e^{\ln(7)}$
   1. 0
   2. 1
   3. 7
   4. e