Difference between revisions of "Math 22 Logarithmic Functions"
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The logarithm <math>log_a x</math> is defined as | The logarithm <math>log_a x</math> is defined as | ||
<math>log_a x=b</math> if and only if <math>a^b=x</math> | <math>log_a x=b</math> if and only if <math>a^b=x</math> | ||
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| + | ==Definition of the Natural Logarithmic Function== | ||
| + | The natural logarithmic function, denoted by <math>ln x</math>, is defined as | ||
| + | <math>ln x=b</math> if and only if <math>e^b=x</math> | ||
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| + | ==Properties of the Natural Logarithmic Function== | ||
| + | Let <math>g(x)=ln x </math> | ||
| + | 1. The domain of <math>g(x)</math> is <math>(0,\infty)</math> and the range of <math>g(x)</math> is <math>(-\infty,\infty)</math> | ||
| + | 2. The x-intercept of the graph of <math>g(x)</math> is <math>(1,0)</math> | ||
| + | 3. The function <math>g(x)</math> is continuous, increasing, and one-to-one. | ||
| + | 4. <math>\lim_{x\to 0^+} g(x)=-\infty</math> and <math>\lim_{x\to\infty} g(x)=\infty</math> | ||
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[[Math_22| '''Return to Topics Page''']] | [[Math_22| '''Return to Topics Page''']] | ||
'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' | ||
Revision as of 07:54, 11 August 2020
Logarithm Function
The logarithm is defined as if and only if
Definition of the Natural Logarithmic Function
The natural logarithmic function, denoted by , is defined as if and only if
Properties of the Natural Logarithmic Function
Let 1. The domain of is and the range of is 2. The x-intercept of the graph of is 3. The function is continuous, increasing, and one-to-one. 4. and
This page were made by Tri Phan