Lecture 3 Flashcards
Logarithms and Exponentials (19 cards)
What are logarithms?
A way to replace multiplication with addition and division with subtraction
How are logarithms written?
log(base)number = power
How can indices show 16 x 64?
16 x 64 = 2⁴ x 2⁶ =2¹⁰
How is 16 = 2⁴ shown as a logarithm
log₂ 16 = 4
What do logarithm below <1 produce?
A negative result e.g. log₁₀ 0.7 = −0.1549
What are the general forms of logarithms?
b = aⁿ then logₐ b = n
When are logarithms positive?
if the base and number is >1
OR
is both between 0 and 1 but not 0 or 1
What are most logs a base to when there is not one?
10
What is the logarithm law if adding logs?
logₐ(AB) = logₐ A + logₐ B
What is the logarithm law if subtracting logs?
logₐ(A/B) = logₐ A - logₐ B
If there is a number in front of log what happens to it?
It becomes the power to the base
What happens if there is no power?
Power is considered 1
What is an exponential function?
f(x) = aˣ
where a >0
What is the base of the exponential function (f(x) = aˣ)?
the number a is the base of the function
If a>1 what is it called?
Exponential Growth
If a<1 what is it called?
Exponential Decay
What is the exponential number?
e = 2.718 also known as Euler’s number, a constant
What is the exponential function for logarithms?
f(x) = logₐ x
What is a natural logarithm?
a log with a base of e
