Convex analysis | Mathematical analysis

Logarithmically concave function

In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it satisfies the inequality for all x,y ∈ dom f and 0 < θ < 1. If f is strictly positive, this is equivalent to saying that the logarithm of the function, log ∘ f, is concave; that is, for all x,y ∈ dom f and 0 < θ < 1. Examples of log-concave functions are the 0-1 indicator functions of convex sets (which requires the more flexible definition), and the Gaussian function. Similarly, a function is log-convex if it satisfies the reverse inequality for all x,y ∈ dom f and 0 < θ < 1. (Wikipedia).

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Graphing a logarithmic function with two reflections

👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value

From playlist How to Graph Logarithmic Functions in Different Bases

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Learn how to graph a logarithm with reflections over x and y axis

👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value

From playlist How to Graph Logarithmic Functions in Different Bases

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Graphing the logarithmic equation with a horizontal & vertical translation

👉 Learn how to graph logarithmic functions involving vertical shift. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x

From playlist How to Graph Logarithmic Functions with Vertical Shift

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Emanuel Milman: 1 D Localization part 4

The lecture was held within the framework of the Hausdorff Trimester Program: Optimal Transportation and the Workshop: Winter School & Workshop: New developments in Optimal Transport, Geometry and Analysis

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From playlist Geometry

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Determining the x intercept of a logarithmic equation

👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value

From playlist How to Graph Logarithmic Functions in Different Bases

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MIT RES.6-012 Introduction to Probability, Spring 2018 View the complete course: https://ocw.mit.edu/RES-6-012S18 Instructor: John Tsitsiklis License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu

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How to use a table to graph logarithmic function

👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value

From playlist How to Graph Logarithmic Functions in Different Bases

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From playlist Michel van Biezen: PRECALCULUS 1-5 - ALGEBRA REVIEW

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Graphing logarithmic equations

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From playlist How to Graph Logarithmic Functions in Different Bases

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From playlist Workshop: High dimensional measures: geometric and probabilistic aspects

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Graphing logarithmic equations

👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value

From playlist How to Graph Logarithmic Functions in Different Bases

Video thumbnail

Graphing logarithmic equations

👉 Learn how to graph logarithmic functions. The logarithmic function is the inverse of the exponential function. To graph a logarithmic function, it is usually very useful to make the table of values of the function. This is done by choosing a range of values of x and then plug the x-value

From playlist How to Graph Logarithmic Functions in Different Bases

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Convex function | Beta distribution | Regular distribution (economics) | Deviation risk measure | Dirichlet distribution | Gamma distribution | Just another Gibbs sampler | F-distribution | Indicator function | Logarithm | Cumulative distribution function | Exponential distribution | Logarithmically convex function | Survival function | Weibull distribution | Domain of a function | Convex analysis | Laplace distribution | Marginal distribution | Multivariate normal distribution | Level set | Logarithmically concave sequence | Pareto distribution | Student's t-distribution | Hyperbolic secant distribution | Bayesian inference using Gibbs sampling | Logarithmically concave measure | Gaussian function | Concave function | Log-normal distribution | Maximum entropy probability distribution | Probability distribution | Chi distribution | Normal distribution | Convolution | Gibbs sampling | Random variable | Cauchy distribution | Normal-gamma distribution | Prékopa–Leindler inequality | Wishart distribution | Convex set | Logistic distribution