Difference between revisions of "Math 22 Exponential Functions"
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==Definition of Exponential Function== | ==Definition of Exponential Function== | ||
If <math>a>0</math> and <math>a\ne 1</math>, then the exponential function with base <math>a</math> is <math>a^x</math> | If <math>a>0</math> and <math>a\ne 1</math>, then the exponential function with base <math>a</math> is <math>a^x</math> | ||
| + | ==Properties of Exponents== | ||
| + | Let <math>a</math> and <math>b</math> be positive real numbers, and let <math>x</math> and <math>y</math> be real numbers. | ||
| + | |||
| + | 1.<math>a^0=1</math> | ||
| + | |||
| + | 2.<math>a^xa^y=a^{x+y}</math> | ||
| + | |||
| + | 3.<math>\frac{a^x}{a^y}=a^{x-y}</math> | ||
| + | |||
| + | 4.<math>(a^x)^y=a^{xy}</math> | ||
| + | |||
| + | 5.<math>(ab)^x=a^xb^x</math> | ||
| + | |||
| + | 6.<math>(\frac{a}{b})^x=\frac{a^x}{b^x}</math> | ||
| + | |||
| + | 7.<math>a^{-x}=\frac{1}{a^x}</math> | ||
| + | |||
| + | |||
[[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 07:15, 11 August 2020
Definition of Exponential Function
If and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a\ne 1}
, then the exponential function with base Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a}
is Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^x}
Properties of Exponents
Let Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle b} be positive real numbers, and let Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y} be real numbers.
1.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^0=1}
2.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^xa^y=a^{x+y}}
3.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{a^x}{a^y}=a^{x-y}}
4.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (a^x)^y=a^{xy}}
5.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (ab)^x=a^xb^x}
6.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (\frac{a}{b})^x=\frac{a^x}{b^x}}
7.Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^{-x}=\frac{1}{a^x}}
This page were made by Tri Phan