exponentials and logs exact values properties and domain and range
TRANSCRIPT
e-2 =
2
1
e=
Answer
ln(3x5) =
Answer
=ln3 + lnx5
=ln3 + 5lnx
eln3=
Answer
= 3
=
6
ln5xy
Answer
6lnln5ln −+= yx
For y=lnx, can x = 0?
Answer
No!Domain of natural log is
),0( ∞
For y=2x, can x be 0?
Answer
Yes!Domain of exponential is
any # to the 0 power is 1(0,1) point on parent graph
),( ∞−∞
For y=2x, can y be negative?
Answer
No!Range of exponential is
),0( ∞
ln0 =
Answer
= undefined
lne2 =
Answer
lne2 = 2lne = 2(1) = 2
ln1 =
Answer
= 0
ln(-2) =
Answer
= undefined
e0 =
Answer
= 1
For y=2x, can x be negative?
Answer
Yes!Domain of exponential is
),( ∞−∞
For y=2x, can y = 0?
Answer
No!Range of exponential is
HA at y=0 (for parent graph)
),0( ∞
For y=lnx, can x be negative?
Answer
No!Domain of natural log is
),0( ∞
For y=lnx, can y = 0?
Answer
Yes!Range of natural log is
(inverse of exponential)(1,0) is a point on the parent
graph
),( ∞−∞
Does ln(x2+1) = lnx2 + ln1 = 2lnx + 0 ?
Answer
NO!It is the natural log of that
quantity.