3.4-7

Question 1

lne=1 as exp

Answer 1

e^1=e

Question 2

is it possibe for a log function to have nagative outputs in the form y=logbx

Answer 2

yes if b is whole and a is fractions

Question 3

is it possibe for a log function to have c<b<a in the form a=logbc

Answer 3

yes when 3=log1/2(1/8)

Question 4

log b definition

Answer 4

b>0

Question 5

parent ln

Answer 5

y=lnx

Question 6

1/x

Answer 6

horzionatal stretch

Question 7

why all graphs of logs pass through (1,0) and (b,1)

Answer 7

b^0=1 and b^1=b)

Question 8

log func graphs must pass thru

Answer 8

(1,0) and (b,1)

Question 9

-log

Answer 9

reflect over x

Question 10

log(-x)

Answer 10

reflect over y

Question 11

writing log equation

Answer 11

find shift, do opposite direction to find base of va

Question 12

va shows

Answer 12

left vs right shift

Question 13

passing thru point

Answer 13

just check

Question 14

how to find inverse of a log from a graph

Answer 14

reflect the original graph across the line (y=x). Another method is to pick a few points on the original log graph, switch the x and y coordinates for each point, and plot these new points to sketch the inverse graph. The inverse of a logarithmic function is always an exponential function.

Question 15

expanding logs with division

Answer 15

al in denominator will be negative

Question 16

relationship between exponent and log properties

Answer 16

both involve addition for products with like bases

Question 17

a/b=e^c

Answer 17

lna/b=c

Question 18

output of a log func

Answer 18

tells you what exponent you must raise the base to in order to arrive at the input

Question 19

log from

Answer 19

logbx=y

Question 20

exp form

Answer 20

b^y=x

Question 21

common log

Answer 21

if no subscript is given, assume b=10

Question 22

natural log

Answer 22

if base is e, logex=lnx

Question 23

domain

Answer 23

(0,inf) since powers of b are always positive

Question 24

range

Answer 24

(-inf, inf) since exponents can be negative or positve

Question 25

relationship between log and inverse exp

Answer 25

domains and range are just inversed

Question 26

transformations affect

Answer 26

x intercept, asymptoes, domain

Question 27

parent log functions

Answer 27

y=logbx for any base b>0 b not equal 1

Question 28

2 key points

Answer 28

(1,0) x intercept (b,1) identity

Question 29

vertical asymptoe

Answer 29

x=0

Question 30

b^x and logbx

Answer 30

inverse

Question 31

expanded form logbx+logby

Answer 31

logbxy

Question 32

expanded logic-logby

Answer 32

log(x/y)

Question 33

alogb^x

Answer 33

logbx^a

Question 34

estimating x^?

Answer 34

choose values in between and guess

Question 35

log negatives

Answer 35

none unless shift

Question 36

strategies for solving exp and logs

Answer 36

apply log properties, ise inverse operationsm, reweire in alternate form to isolate variable

Question 37

one to one property

Answer 37

if b^x=b^y, x=y and if logbx=logby then x=y so same output means same inpout

Question 38

uusing calculator

Answer 38

find intersectoion of two graphs

Question 39

x^1/2

Answer 39

root x

Question 40

use ln as

Answer 40

log with e to undo exponential increase

Question 41

use answer in exponential form

Answer 41

then set equal to other exponential

Question 42

look at x interept using calculator then

Answer 42

insert both sides of equation

Question 43

order for transformations

Answer 43

h shift, y stretch/reflect, h stretch/reflect, v shift

Question 44

reflect over x

Answer 44

x,y to x,-yl

Question 45

log domain and range

Answer 45

range always inf, domain is ^(x+this value) to inf

Question 46

exp domain and range

Answer 46

domain always inf, range is + his value to inf

Question 47

log transfoamations

Answer 47

change log to f(x)