Exponents and logarithms

Extend exponent types and interpret logarithms through powers.

Meaning

Exponents extend repeated multiplication. A logarithm gives the exponent needed to obtain a number from a base. For real logarithms, the base is positive and not 1, and the argument is positive.

Example

Since The logarithm asks for the exponent in that power relationship.Since 8=2³ and 4=2², their product is 2⁵, so log₂(8×4)=3+2. The logarithm product law follows from adding exponents when multiplying powers with the same base. cannot be split into The product law applies to products of positive arguments.

Practice for this concept

Scope and references

Topics

Extending exponents, logarithm meaning and laws, common logarithms

Learning goal

Extend exponent types and interpret logarithms through powers.

Helpful background

Explore powers and conditions for exponent laws.