Vocab
what is the value of the log if the base and the argument are the same?
1
T or F: logarithms are continuous and increasing from 0 to infinity
describe the transformations: -2 + log(x-3)
down two units, to the right 3 units
T or F: e is an irrational number
true
what is the inverse of x-3
x+3
if the argument is 1, what is the value of the log
0
which value is the argument: log25
5
where is the vertical asymptote for logs?
x = 0
what is the value of e? i need at least 3 decimal places.
2.718281828...
what is the inverse of 3x
x/3
if the argument is a common fraction, what sign will the answer have?
negative
how can you expand this log based off the power rule: logx3
3logx
what is the domain of a log?
(0,infinity)
T or F: the domain/range for e is all real numbers
False, the domain is all real numbers but the range for e is (0,infinity), e cannot have any negative numbers
what is the inverse of x2
square root of x
if the arguments are equal, the log with the smaller base will be larger or smaller?
larger
how can you expand this function using the product rule: log(ab)
log a + log b
what is the range of a log?
all real numbers or (-infinity, infinity)
what is the inverse of e?
natural log (ln)
what is the inverse of y=3x+9
y = (x-9) / 3
what is the notation for estimating a log? use variables x and y
it is between x and y but closer to x/y
how do you expand this expression using the quotient rule: log(a/b)
log a - log b
describe the transformation: log(x+3) +4
up 4 units, to the left 3 units
T or F: e is increasing over the entire domain and has the same shape as y=3x
True, it is similar to 3 since e = 2.7 and is increasing
what is the inverse of 2y = 2x - 10
y = x - 5