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# What is the difference between exponential and logarithmic graphs?

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

This section is about the inverse of the exponential function. The inverse of an exponential function is a logarithmic function….Comparison of Exponential and Logarithmic Functions.

Exponential Logarithmic
Function y=ax, a>0, a≠1 y=loga x, a>0, a≠1
Domain all reals x > 0
Range y > 0 all reals

## Which is the graph of a logarithmic function?

The graph of a logarithmic function has a vertical asymptote at x = 0. The graph of a logarithmic function will decrease from left to right if 0 < b < 1. And if the base of the function is greater than 1, b > 1, then the graph will increase from left to right.

What’s the difference between exponential and logarithmic functions?

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.

### Is logarithmic the same as exponential?

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. So you see a logarithm is nothing more than an exponent.

How do you read logarithmic functions?

The word logarithm, abbreviated log, is introduced to satisfy this need. This equation is rewritten as y = log 2 x. This is read as “ y equals the log of x, base 2” or “ y equals the log, base 2, of x.” which is read “ y equals the log of x, base b” or “ y equals the log, base b, of x.”

## What are the steps to graph a logarithmic function?

Graphing Logarithmic Functions

1. Step 1: Find some points on the exponential f(x). The more points we plot the better the graph will look.
2. Step 2: Switch the x and y values to obtain points on the inverse.
3. Step 3: Determine the asymptote.
4. Graph the following logarithmic functions. State the domain and range.

## What are logarithmic functions used for in real life?

Using Logarithmic Functions Much of the power of logarithms is their usefulness in solving exponential equations. Some examples of this include sound (decibel measures), earthquakes (Richter scale), the brightness of stars, and chemistry (pH balance, a measure of acidity and alkalinity).

How do you graph a log function?

Consider the logarithmic function y = [ log 2 ( x + 1 ) − 3 ] . This can be obtained by translating the parent graph y = log 2 ( x ) a couple of times. Consider the graph of the function y = log 2 ( x ) . Since h = 1 , y = [ log 2 ( x + 1 ) ] is the translation of y = log 2 ( x ) by one unit to the left. Now, k = − 3 .

### How do you calculate natural log?

You can use the natural logarithm function (LN, the shifted function of the 2 key) to compute the common logarithm of a number using the relationship. log(x) = ln(x)/ln(10) In words, calculate the natural log of the value and divide it by the natural log of ten.

### What is exponential log?

The log form and exponential form are actually inverses of each other. Exponentials happen when a number is raised to a certain power. It is a shorter way to show that a number is repeatedly multiplied a number of times by itself.

What are the properties of logs?

Logs have four basic properties: Product Rule: The log of a product is equal to the sum of the log of the first base and the log of the second base (). Quotient Rule : The log of a quotient is equal to the difference of the logs of the numerator and denominator (). Power Rule : The log of a power is equal to the power times the log of the base ().