Exponential and Logarithmic Equations Lecture Notes

These flashcards cover key concepts related to exponential and logarithmic equations, their properties, and how to manipulate and solve them.

What is the goal when solving exponential and logarithmic equations?

The goal is to isolate the variable.

What can cancel each other when they have the same base in logarithmic equations?

Exponential and logarithmic functions can cancel each other.

What do you need to check when using logarithms?

You need to check the domain, as logarithms are 'picky eaters'.

What is the Product Property of logarithms?

logb(uv) = logb(u) + log_b(v) for any u and v.

What is the quotient property of logarithms?

logb(u/v) = logb(u) - log_b(v) for any u and v.

What is an example of an exponential equation?

Example: 3*2 + 7 = 6 is an exponential equation.

How can you express x=125 in logarithmic form?

log_x(125) = 3.

What is the change of base formula for logarithms?

logb(a) = logk(a) / log_k(b) for a new base k.

How do you express log_a k = 2 in exponential form?

a^2 = k.

What is exponential growth represented by?

P(t) = P0 (1 + r)^t where P0 is the initial quantity and r is the growth rate.

How does one determine how long it takes to produce a certain number of amoebas?

Use the formula t = log_b(N) where N is the desired number of amoebas.