Exponentials and logs exact values properties and domain and range
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Transcript of Exponentials and logs exact values properties and domain and range
![Page 1: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/1.jpg)
e-2 =
![Page 2: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/2.jpg)
2
1
e=
Answer
![Page 3: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/3.jpg)
ln(3x5) =
![Page 4: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/4.jpg)
Answer
=ln3 + lnx5
=ln3 + 5lnx
![Page 5: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/5.jpg)
eln3=
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Answer
= 3
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=
6
ln5xy
![Page 8: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/8.jpg)
Answer
6lnln5ln −+= yx
![Page 9: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/9.jpg)
For y=lnx, can x = 0?
![Page 10: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/10.jpg)
Answer
No!Domain of natural log is
),0( ∞
![Page 11: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/11.jpg)
For y=2x, can x be 0?
![Page 12: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/12.jpg)
Answer
Yes!Domain of exponential is
any # to the 0 power is 1(0,1) point on parent graph
),( ∞−∞
![Page 13: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/13.jpg)
For y=2x, can y be negative?
![Page 14: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/14.jpg)
Answer
No!Range of exponential is
),0( ∞
![Page 15: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/15.jpg)
ln0 =
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Answer
= undefined
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lne2 =
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Answer
lne2 = 2lne = 2(1) = 2
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ln1 =
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Answer
= 0
![Page 21: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/21.jpg)
ln(-2) =
![Page 22: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/22.jpg)
Answer
= undefined
![Page 23: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/23.jpg)
e0 =
![Page 24: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/24.jpg)
Answer
= 1
![Page 25: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/25.jpg)
For y=2x, can x be negative?
![Page 26: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/26.jpg)
Answer
Yes!Domain of exponential is
),( ∞−∞
![Page 27: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/27.jpg)
For y=2x, can y = 0?
![Page 28: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/28.jpg)
Answer
No!Range of exponential is
HA at y=0 (for parent graph)
),0( ∞
![Page 29: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/29.jpg)
For y=lnx, can x be negative?
![Page 30: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/30.jpg)
Answer
No!Domain of natural log is
),0( ∞
![Page 31: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/31.jpg)
For y=lnx, can y = 0?
![Page 32: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/32.jpg)
Answer
Yes!Range of natural log is
(inverse of exponential)(1,0) is a point on the parent
graph
),( ∞−∞
![Page 33: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/33.jpg)
Does ln(x2+1) = lnx2 + ln1 = 2lnx + 0 ?
![Page 34: Exponentials and logs exact values properties and domain and range](https://reader033.fdocuments.us/reader033/viewer/2022052601/559771b01a28ab520e8b47bc/html5/thumbnails/34.jpg)
Answer
NO!It is the natural log of that
quantity.