LOGARITHMIC FUNCTIONS Flashcards
𝑥 = 𝑏^y is known as a _________ function
logarithmic
definition of a logarithmic function with base b
f(x) = logb (x)
x > 0, b > 0, b ≠ 1
log𝑒 𝑥 is called “______________” with base e
natural logarithm
log𝑒 𝑥 can be simplified by the notation ____
ln x
Properties of Logarithms
logb b = 1
logb 1 = 0
logb (b)^x = x
b^(logb x) = x; x > 0
Laws of Logarithms
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
logarithmic functions can be written as a ______ of same bases
quotient
to write the logarithmic functions in a different base, we use the ________ formula
change of base
what is the change of base formula
log𝑏 𝑀 = (log𝑎 𝑀/ log𝑎 𝑏)
what is the domain of logarithmic functions
set of all positive non-zero real numbers
what is the range of logarithmic functions
set of all real numbers
intercepts of logarithmic functions
x-intercept at (a,0)
no y-intercept
what is the asymptote of logarithmic functions
y axis
sample points for logarithmic functions
(𝑎𝑏, 1) 𝑎𝑛𝑑 (𝑎/𝑏, −1)
a logarithmic function is _________ when b > 1 and ________ when 0 < b < 1
increasing; decreasing
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
Charles Richter
formula for magnitude
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)
the decibel (dB) level of sound in acoustics is given by what formula
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
the pH level of any water-based solution is determined by what formula
𝑝𝐻 = − log(𝐻⁺)
where 𝐻⁺ is the concentration of hydrogen ions in
moles per liter
