logarithmic functions mr. velazquez honors precalculus · pdf filedefinition of the...
TRANSCRIPT
![Page 1: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/1.jpg)
LOGARITHMIC FUNCTIONS Mr. Velazquez
Honors Precalculus
![Page 2: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/2.jpg)
DEFINITION OF LOGARITHMIC FUNCTIONS
![Page 3: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/3.jpg)
LOGARITHMIC AND EXPONENTIAL FORMS
To change from logarithmic to the more familiar exponential
form, use the following pattern:
(start here)
![Page 4: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/4.jpg)
BASIC LOGARITHMIC PROPERTIES
Examples: log8 8 = 1 log6 1 = 0
Examples: log7 72 = 2 5log58 = 8
![Page 5: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/5.jpg)
GRAPHS OF LOGARITHMS
![Page 6: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/6.jpg)
GRAPHS OF LOGARITHMS
![Page 7: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/7.jpg)
GRAPHS OF LOGARITHMS
![Page 8: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/8.jpg)
EXAMPLE:
![Page 9: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/9.jpg)
EXAMPLE:
![Page 10: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/10.jpg)
EXAMPLE:
![Page 11: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/11.jpg)
DOMAIN AND RANGE
EXAMPLE: Find the domain and range of 𝑓 𝑥 = log4 𝑥 − 5
![Page 12: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/12.jpg)
THE COMMON LOGARITHM
![Page 13: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/13.jpg)
THE COMMON LOGARITHM
![Page 14: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/14.jpg)
THE NATURAL LOGARITHM
![Page 15: LOGARITHMIC FUNCTIONS Mr. Velazquez Honors Precalculus · PDF fileDefinition of the Logarithmic Function For x > O and b > O, b 1, y = logb x is equivalent to bY — x The function](https://reader031.vdocuments.site/reader031/viewer/2022030411/5a9dc6207f8b9ae0108b62c3/html5/thumbnails/15.jpg)
CLASSWORK & HOMEWORK
Homework:
Pg. 410, #1-45
(odds)