1.2 Indices and Logarithms

• state and apply the laws of indices
• work with zero, negative and fractional indices
• relate indices to logarithms
• use logarithms to solve simple equations

“How can very large and very small numbers be written briefly?”

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1. The laws of indices
   40 min · 2 practice tasks · quiz
   A shorthand for repeated multiplication, and the rules that follow from it.
2. Introducing logarithms
   40 min · 2 practice tasks · quiz
   Reading an index question backwards, and why that turns out to be useful.
3. Zero and negative indices
   40 min · 1 practice tasks · quiz
   Why a to the power 0 is 1, and why a negative index is a reciprocal, not a negative number.
4. Fractional indices
   40 min · 1 practice tasks · quiz
   A fractional index is a root, then a power: the denominator is the root.
5. Combining the laws of indices
   40 min · 1 practice tasks · quiz
   Rewrite different-looking bases as the same prime, then add, subtract or multiply the indices.
6. Common logarithms
   40 min · 1 practice tasks · quiz
   A common logarithm is the power of 10; log with no base written means base 10.
7. The laws of logarithms
   40 min · 1 practice tasks · quiz
   Logs turn a product into a sum, a quotient into a difference, and a power into a multiplication.
8. Computing with common logarithms
   40 min · 1 practice tasks · quiz
   Multiply, divide, raise to a power and take a root by adding, subtracting or scaling logs, then taking the antilog.