Unit 2 B Flashcards
log function general form
f(x)=alog(b)x
a does not = 0
b > 0
domain of general log function
(0, inf)
cannot take the log of a negative number
range of general log function
(-inf, +inf)
like a square root
if a > 0 and b >1
cd, growth
VA of reg log
x = 0
if a < 0 and b > 1
reflection over x axis
cu, decay
increasing vs. decreasing
only one!
no relative extrema unless on a closed interval
cu vs. cd
only one!
no points of inflection
end behavior limit statements of a log
left as x –> 0 (+/-)
right as x –> inf
logs in table
x values change proportionally
product property of logs
log(b)xy = log(b)x + log(b)y
quotient property of logs
log(b)x/y = log(b)x - log(b)y
power property of logs
log(b)x^m = m*log(b)x
to use power rules of logs…
bases (b) must be the same
b^log(b)c =
c
log(b)b^a =
a
change of base property of logs
log(b)a = log(c)a/log(c)b
natural logarithm function
lnx
lnx =
log(e)x
log graph
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product property of exponents
b^m*b^n=b^(m+n)
power property of exponents
(b^m)^n=b^m*n
negative exponent property
b^-n=1/b^n
if logs have the same base and are set equal to each other…
can cancel log
when solving logs, remember to…
check for extraneous solutions!
- negative number
- zero
log of a proper fraction
negative
equations with multiple exponential functions
find common bases using the properties of exponents
if the bases of exponential functions are the same
cancel base and set exponents equal to eachother
quadratic formula
[-b+/-(sqrt : b^2-4ac)]/2a
general form of exponential
f(x) = ab^(x+h)+k
general form of log
f(x)=alog(b)(x+h)+k
when finding inverses make sure to..
use correct inverse notation!
solving logarithmic inequalities
combine log
change forms
undo fraction
move to one side
factor
put zeros and undefined values on sign chart
test points
in a semi-log plot
y axis is logarithmically scaled
exponential functions will appear lineasr
linear equation for semi log plot
y = logbx+loga
slope : logb
y-int : loga
base = the base of the vertical axis
f(g(x)) is the same as
fog(x)
inverse graph
reflection over y=x
inverses if…
f(g(x))=x & g(f(x))=x
exponential is just…
logarithmic rewritten
b^c=a
log(b)a=c
log table
ex. but switched
x changes proportionally
if f(x)=b^x and g(x)=log(b)x
they are inverses
log(b)b^a=
a
log form
f(x) = alog(b)x
b^log(b)c=
c
