The decibel scale is logarithmic. Can you perform operations with expressions that have different bases but the same exponent?
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what are indices in maths Informational
- The laws of logarithms are derived from the laws of indices.
- What is the limit of $a^x$ as $x \to \infty$ for $a > 1$?
- Number lines to illustrate positive and negative exponents.
- Using the same definitions, $xy = b^m \times b^n = b^{m+n}$, so $\log_b (xy) = m+n = \log_b y + \log_b x$. Can you explain the quotient rule for logarithms using the quotient rule for indices?
- Working with irrational exponents. Proving identities involving indices.
- What are prefixes like milli, micro, nano related to negative powers of 10? How are indices used in logarithms with different bases?
- Give an example of a differential equation with an exponential solution. How are indices used in integration involving exponential functions?
- How are indices related to logarithms?
- Spread of information or viruses. How can you model real-world situations using exponential functions?
- Rationalize $\frac{2}{1+\sqrt{3}}$. Rationalize $\frac{\sqrt{5}-1}{\sqrt{5}+1}$.
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