LOGARITHMIC FUNCTIONS

Question 1

𝑥 = 𝑏^y is known as a _________ function

Answer 1

logarithmic

Question 2

definition of a logarithmic function with base b

Answer 2

f(x) = logb (x)

x > 0, b > 0, b ≠ 1

Question 3

log𝑒 𝑥 is called “______________” with base e

Answer 3

natural logarithm

Question 4

log𝑒 𝑥 can be simplified by the notation ____

Answer 4

ln x

Question 5

Properties of Logarithms

Answer 5

logb b = 1
logb 1 = 0
logb (b)^x = x
b^(logb x) = x; x > 0

Question 6

Laws of Logarithms

Answer 6

PRODUCT LAW:
log𝑏 𝑀𝑁 = log𝑏 𝑀 + log𝑏 𝑁
QUOTIENT LAW:
log𝑏(𝑀/𝑁)= log𝑏 𝑀 − log𝑏 𝑁
POWER LAW:
log𝑏 𝑀^𝑝 = 𝑝 log𝑏 𝑀

Question 7

logarithmic functions can be written as a ______ of same bases

Answer 7

quotient

Question 8

to write the logarithmic functions in a different base, we use the ________ formula

Answer 8

change of base

Question 9

what is the change of base formula

Answer 9

log𝑏 𝑀 = (log𝑎 𝑀/ log𝑎 𝑏)

Question 10

what is the domain of logarithmic functions

Answer 10

set of all positive non-zero real numbers

Question 11

what is the range of logarithmic functions

Answer 11

set of all real numbers

Question 12

intercepts of logarithmic functions

Answer 12

x-intercept at (a,0)

no y-intercept

Question 13

what is the asymptote of logarithmic functions

Answer 13

y axis

Question 14

sample points for logarithmic functions

Answer 14

(𝑎𝑏, 1) 𝑎𝑛𝑑 (𝑎/𝑏, −1)

Question 15

a logarithmic function is _________ when b > 1 and ________ when 0 < b < 1

Answer 15

increasing; decreasing

Question 16

in 1935, he proposed a logarithmic scale to measure the intensity of an earthquake. He defined the magnitude of an earthquake as a function of its amplitude on a standard seismograph

Answer 16

Charles Richter

Question 17

formula for magnitude

Answer 17

R = (2/3) log(E / 10^(4.40))
where E (in joules) is the energy released by the
earthquake (the quantity 10^(4.40) joules is the energy
released by a very small reference earthquake)

Question 18

the decibel (dB) level of sound in acoustics is given by what formula

Answer 18

D = 10log(I / 10^-12)
where I is the sound intensity in 𝑤𝑎𝑡𝑡𝑠/𝑚^2
the quantity 10−12 𝑤𝑎𝑡𝑡𝑠/𝑚^2 is least audible sound a human can hear

Question 19

the pH level of any water-based solution is determined by what formula

Answer 19

𝑝𝐻 = − log(𝐻⁺)
where 𝐻⁺ is the concentration of hydrogen ions in
moles per liter