1.3 Indices and Logarithms

• Numbers in index form
• Laws of indices
• Powers of 10 to common logarithms

• express numbers in index form in different situations
• generate the laws of indices in different situations
• apply the laws of indices in different situations
• relate powers of 10 to common logarithms in different situations
• appreciate the use of indices and logarithms in real-life situations

“How do we express numbers in powers?”

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1. Index form: base and index
   40 min · 1 practice tasks · quiz
   A number in index form is a base with an index. The index counts equal factors of the base.
2. Multiply powers: add the indices
   40 min · 1 practice tasks · quiz
   When the bases are the same, multiply powers by adding the indices. Generate the law by expanding factors.
3. Divide powers: subtract the indices
   40 min · 1 practice tasks · quiz
   When the bases are the same, divide powers by subtracting the indices. Cancel equal factors.
4. Power of a power: multiply the indices
   40 min · 1 practice tasks · quiz
   A power raised to a power multiplies the indices. Expand as a repeated product of the inner power.
5. Zero index and index one
   40 min · 1 practice tasks · quiz
   Any non-zero number to the power 0 is 1. A number to the power 1 is itself. Generate a^0 from the division law.
6. Powers of 10 and common logarithms
   40 min · 1 practice tasks · quiz
   A common logarithm is the index when a number is written as a power of 10. Read it from the power, from tables, or from a calculator.