Study Notes
Integer exponents are exponents that are whole numbers, which can be positive or negative, indicating how many times the base number is multiplied by itself. Logarithms answer the question of how many times one number must be multiplied by itself to reach another number.
- Integer Exponents — whole number exponents that indicate repeated multiplication of a base. Example: In 2^3, the base 2 is multiplied by itself 3 times to get 8.
- Fractional Exponents — exponents that are fractions, representing roots of numbers. Example: 8^(1/3) is the cube root of 8, which equals 2.
- Logarithms — the power to which a base number must be raised to produce a given number. Example: log base 2 of 8 is 3 because 2^3 = 8.
Exam Tips
Key Definitions to Remember
- Integer exponents are whole numbers used as exponents.
- Logarithms determine how many times a base is multiplied to reach a number.
Common Confusions
- Confusing fractional exponents with negative exponents.
- Misunderstanding the base in logarithms.
Typical Exam Questions
- Express 5^3 = 125 in logarithm form? Answer: log base 5 of 125 is 3.
- Express log base 10 of 1 = 0 in exponential form? Answer: 10^0 = 1.
- Find the log of 32 to the base 4? Answer: log base 4 of 32 is 5/2.
What Examiners Usually Test
- Conversion between exponential and logarithmic forms.
- Simplifying expressions with exponents and logarithms.