# How do you determine if a function is logarithmic or exponential?

Table of Contents

- 1 How do you determine if a function is logarithmic or exponential?
- 2 What is the difference between exponential function and logarithmic function?
- 3 What is the relation between logarithmic function and exponential function?
- 4 How do we know when a function indicates an exponential growth or exponential decay?
- 5 What are the exponential and logarithm functions in calculus?
- 6 What is the differentiation formula for expexponential functions?

## How do you determine if a function is logarithmic or exponential?

The inverse of an exponential function is a logarithmic function. Remember that the inverse of a function is obtained by switching the x and y coordinates. This reflects the graph about the line y=x. As you can tell from the graph to the right, the logarithmic curve is a reflection of the exponential curve.

## What is the difference between exponential function and logarithmic function?

The exponential function is given by ƒ(x) = ex, whereas the logarithmic function is given by g(x) = ln x, and former is the inverse of the latter. The domain of the exponential function is a set of real numbers, but the domain of the logarithmic function is a set of positive real numbers.

**What is the difference between exponential and logarithmic growth?**

Exponential growth is where the rate of increase in something is proportional to the amount present. ie . This has a solution of the form and hence the term “exponential”. Logarithmic growth is where the rate of increase in something is inversely proportional to the amount of time that has expired.

**What is the relationship between exponential & logarithmic equations and E & LN?**

The natural logarithm is the inverse of the exponential function f(x)=ex f ( x ) = e x . It is defined for e>0 , and satisfies f−1(x)=lnx f − 1 ( x ) = l n x . As they are inverses composing these two functions in either order yields the original input.

### What is the relation between logarithmic function and exponential function?

You can see straight away that the logarithm function is a reflection of the exponential function in the line represented by f(x) = x. In other words, the axes have been swapped: x becomes f(x), and f(x) becomes x. The exponential function f(x) = ex is the inverse of the logarithm function f(x) = ln x.

### How do we know when a function indicates an exponential growth or exponential decay?

If a is positive and b is greater than 1 , then it is exponential growth. If a is positive and b is less than 1 but greater than 0 , then it is exponential decay.

**What is the relationship between exponential and logarithmic functions How might these functions relate to the study of calculus?**

Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = ax is x = ay. The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay.

**What is the difference between exponential and logarithmic differentiation?**

Differentiation of Exponential and Logarithmic Functions Exponential functions and their corresponding inverse functions, called logarithmic functions, have the following differentiation formulas: Note that the exponential function f (x) = e x has the special property that its derivative is the function itself, f ′ (x) = e x = f (x).

## What are the exponential and logarithm functions in calculus?

The most common exponential and logarithm functions in a calculus course are the natural exponential function, ex e x, and the natural logarithm function, ln(x) ln. . ( x). We will take a more general approach however and look at the general exponential and logarithm function.

## What is the differentiation formula for expexponential functions?

Exponential functions and their corresponding inverse functions, called logarithmic functions, have the following differentiation formulas: Note that the exponential function f( x) = e x has the special property that its derivative is the function itself, f′( x) = e x = f( x).

**How do you find the derivative of a logarithmic function?**

The derivative is given as where ln (b) or log e b is the natural logarithm of b. This is a standard logarithm function. It has the base = e = 2.71828. Its derivative – since ln (e) = 1. We have already told you that the logarithmic and the exponential functions are inverses of each other.