## Is the log of a convex function convex?

# Is the log of a convex function convex?

## Is the log of a convex function convex?

The Bohr–Mollerup theorem characterizes the Gamma function Γ(x) as the unique function f(x) on the positive reals such that f(1)=1, f(x+1)=xf(x), and f is logarithmically convex, i.e. log(f(x)) is a convex function.

**Is sum of log convex?**

The LogSumExp function is convex, and is strictly increasing everywhere in its domain (but not strictly convex everywhere). which means the gradient of LogSumExp is the softmax function. The convex conjugate of LogSumExp is the negative entropy.

### How do you calculate log sum?

A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, logb(xy)=logb(x)+logb(y).

**What is the sum of a log?**

The sum of the logs is the log of the product. The log of a sum cannot be simplified. The log of a difference is NOT the difference of the logs. The difference of the logs is the log of the quotient.

#### Is log a concave function?

Logarithm is Strictly Concave – ProofWiki.

**What is log a B?**

log A + log B = log AB. This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB. For example, we can write. log10 5 + log10 4 = log10(5 × 4) = log10 20.

## What does log mean in algebra?

A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2.

**How do you know if a function is concave or convex?**

To find out if it is concave or convex, look at the second derivative. If the result is positive, it is convex. If it is negative, then it is concave. To find the second derivative, we repeat the process using as our expression.