Logarithmic Functions

what points can be assumed with the equation of an exponential function given

(0,1),(1,a),(-1,1/a)

how do you pick points for graphing

-2,-1,0,1,2, if you raise it to a negative you put it in a fraction and then get the decimal

log1 base a=

0

what can you say about the domain of the inverse

0<y<infinity

what is the range of an exponential function

0<y<infinity

loga base a=

1

when dealing with inverses, if you are given a parenthesis such as (1-x) in the problem what do you do?

IF and only if in parenthesis you leave the 1+x in front

what can you say about the range of the inverse

all real numbers

what is the domain of an exponential function

all real numbers

when graphing logarithmic functions how do you do it?

find the inverse of the function and then graph the exponential form of it

logarithmic rules

get ready

if you have e^-2x=1/3 what do you get

ln1/3/2x

how else can you write log M/N base a?

log M base a minus log N base a

how else can you write logMN base a?

log M base a plus log N base a

how else can you write log4x base 4?

log4 base 4 plus log x base 4 or 1 plus log x base x

is there a y-intercept

no

loga^r base a=

r, what power a is raised too is the answer

how else can you write log M^r base a?

rlogM base a

how do u find the inverse

switch the y and x ("innerchange")

equation of an exponential function

y=a^x, where a>0

x=a^y

y=logX base a

is there an asymptote

yes horizontal of y=0

is there an x intercept, if so what is it

yes, (1,0)

how do you do 2 x 10^2-x=5

you divide by 2 on either side and are left with 10^2-x=5/2 and then you bring the 10 over which is log and then bring the 2-x so its 2-log5/2

how do you do the problem 5e^.2x=7

you divide by 5 on either side and you're left with e^.2x=7/5 and then you move the e over so its ln7/5 and then move the .2x over and you get .2xln7/5

if in a logarithmic function yo are given for example, e^2x+5=8, what do you get and how did you get it

you get ln8-5 over 2

with a simple logarithmic function, how do you solve for x?

you move the number or constant next to Log by its self on one side of the equal sign and then the little subscript you put raised to the power of whatever was first placed behind the equal sign, then solve.

how do you do log(1/9) base 3=-2

you put 3^-2=1/9

how do you solve for x in the problem log4 base x=2

you put the subscript over the number on the other side of the equation so you get x^2=4, which is 2