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Questions and Answers
What is the value of $2^{4}$?
Which of the following represents the cube of 3?
What is the approximate value of log₂64?
What is the value of $2^{1/2}$?
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Which of the following is the value of log₁₀2?
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What is the inverse of 5, denoted as $5^{-1}$?
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What is the approximate value of log₂20100?
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What is the value of $2^{3}$?
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Which logarithmic function returns a value of 0?
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For the logarithmic function log₂6, what is its approximate value?
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Study Notes
Powers of 2
- $2^{-1} = \frac{1}{2}$, $3^{-1} = \frac{1}{3}$, $5^{-1} = \frac{1}{5}$, $7^{-1} = \frac{1}{7}$, $9^{-1} = \frac{1}{9}$, $10^{-1} = \frac{1}{10}$
- $2^{\frac{1}{2}} = \sqrt{2}$
- $2^{\frac{2}{3}} = \sqrt[3]{4}$
- $2^2 = 4$, $2^3 = 8$, $2^4 = 16$
Cubes of Numbers
- $1^3 = 1$, $2^3 = 8$, $3^3 = 27$, $4^3 = 64$, $5^3 = 125$, $6^3 = 216$, $7^3 = 343$, $8^3 = 512$, $9^3 = 729$, $10^3 = 1000$
Table of Powers of 2
- The table lists values of $2^n$ from $2^0$ to $2^{10}$.
- $2^0 = 1$, $2^1 = 2$, $2^2 = 4$, $2^3 = 8$, $2^4 = 16$, $2^5 = 32$, $2^6 = 64$, $2^7 = 128$, $2^8 = 256$, $2^9 = 512$, $2^{10} = 1024$
Table of Powers
- The table shows values for $n^1$ to $n^{10}$ for various values of n (3, 4, 5, 6, 7, 8, 9, 10)
- The table is incomplete and contains missing data
Logarithm Fundamentals
- Logarithm tables and calculators can be used to determine logarithm values
- Logarithms are defined with different bases, including log₁₀, log₂, log₃.
Practice Problems
- The document includes examples and worked problems to help practice calculating logarithms
- The problems involve applying log rules to simplify expressions, such as log(a * b) = log a + log b, log(a / b) = log a - log b, log(ax) = x * log a, loga(x) = log x / log a, log₁₀ x = log x.
- Example calculations include:
- log(625) = log(5⁴) = 4 * log 5
- log(1029) = log(10² * 10⁹ * 10⁻⁴³) = 2 + 9 + (-4)3
- log(5 x 10⁻¹) = log 5 + log 10⁻¹ = 0.7 - 1
- log(6 x 10⁷) = log 6 + log 10⁷ = 0.78 + 7
- log(6 x 10⁻¹) = log 6 + log 10⁻¹ = 0.78 - 1
- Some of the calculations in the examples are incomplete and marked with
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Description
This quiz covers the fundamentals of powers, specifically exploring the powers of 2 and cubes of numbers. It also includes logarithmic concepts and their applications. Test your understanding of these essential mathematical topics.
