5 natural logarithms and y=e^x

Question 1

what does e actually equal

Answer 1

1/0! + 1/1! + 1/2! +1/3! + ……

Question 2

if 2=e^x

what does x=

Answer 2

x=loge2

x=ln2

Question 3

e^x =y

x=

Answer 3

x=lny

Question 4

e^lny = y

x=

Answer 4

x=lne^x

Question 5

lna +lnb=

Answer 5

lnab

Question 6

lna-lnb=

Answer 6

ln(a/b)

Question 7

lna^k=

Answer 7

klna

Question 8

lnx^3

x=

Answer 8

x=e^(7/3)

Question 9

4ln(x-1) -lnx =

Answer 9

ln((x-1)^4/lnx))

Question 10

ln(2x-1) +ln3 = 2

x=

Answer 10

x= 1/6(e^2 +3)

Question 11

e^0 =

Answer 11

1

Question 12

sketch y=e^x graph

Answer 12

never touches the x axis (unless translated), crosses aat y=1

Question 13

draw y=e^(x-1) -3

Answer 13

y=0, x=ln3+1
x=0, y=1/e -3

it is y=e^x translated by (1/-3)

Question 14

inverse of y=e^x

Answer 14

y=lnx

never touches the y axis and crosses the x axis at x=1

Question 15

draw ln(2x +5)

Answer 15

x=0, y=ln5

y=0, x=-2

Question 16

y=lnx asymptote

Answer 16

x=0

Question 17

y=ln(2x-5)ASYMPTOTE

Answer 17

X= -5/2

Question 18

draw y=e^3x and y=3e^-x on the same graph

Answer 18

y=e^3x is a stretch in x direction s.f (1//3)
y=3e^-x is a stretch in y direction s.f 3 with a y axis reflection

find intersection e^3x=3e^-x
x= 1/4 ln3

Question 19

f(x)= e^x +1

it’s inverse

Answer 19

f^-1(x) =ln(x-1)

Question 20

f(x)= ln(3x) -6

it’s inverse

Answer 20

f^-1(x) = 1/3(e^(x+6))

Question 21

g(x)=2e^(x-5) +3
it’s inverse
its domain and range

Answer 21

g^-1(x) = ln(1/2(x-3)) +5
g’s range: g(x) >3 and domain: x E R
g^-1’s range: g^-1 E R and domain: x>3

Question 22

e^2x X e^2x =

Answer 22

e^4x