Product property of logarithms: $$\log_b(mn) = \log_b(m) + \log_b(n)$$

Allows the expansion of logarithms of products.

Quotient property of logarithms: $$\log_b(\frac{m}{n}) = \log_b(m) - \log_b(n)$$

Allows the expansion of logarithms of quotients.

Power property of logarithms: $$\log_b(m^p) = p \cdot \log_b(m)$$

Allows the simplification of logarithms of powers.

Definition of exponential function: $$f(x) = b^x$$ where $$b > 0$$ and $$b \neq 1$$

Exponential functions model growth and decay.

Natural logarithm: $$\ln(x) = \log_e(x)$$

Logarithm with base e, where e is approximately 2.718.

Common logarithm: $$\log_{10}(x)$$

Logarithm with base 10, often written as $$\log(x)$$ .

If $$a = b^c$$ , then $$c = \log_b(a)$$

This shows the relationship between exponentials and logarithms.

Exponential growth formula: $$y = y_0 e^{kt}$$

Models growth where y_0 is the initial amount, k is the growth rate, and t is time.

Chapter 5 Exponentials and Logarithms Test Review Flashcards

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