Solving complex exponential equations.
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what are indices in maths Informational
- A larger base leads to faster growth.
- Solving exponential equations.
- Simplify $\sqrt{50}$ using indices. How do you multiply surds?
- Simplifying expressions with indices.
- Formulas for present and future value involve discount and interest rates raised to powers. How are indices used in economic models (e.g., production functions)?
- Simplify $((a^2)^3)^4$.
- Simplify $(m^{-1})^{-3}$. Simplify $(3a^2b)^2$.
- Using the definition of repeated multiplication. Using mathematical induction for integer exponents. How does the concept of indices relate to the fundamental theorem of algebra? How are indices used in the definition of eigenvalues and eigenvectors of a matrix? How are indices used in the theory of Lie groups and Lie algebras? What are some connections between indices and other areas of mathematics that we haven't discussed yet?
- If $y = a^x$, then $x = \log_a y$. How can you estimate the value of numbers raised to large powers?
- What are the units for volume related to indices? How are indices used in physics (e.g., laws involving squares and cubes)?
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