Inverse Log Graph

Inverse:

The inverse of the given function can be described as the undo of the initial action of the function. All the function has its inverse. But not every inverse is a function.

Log:

The log is a math concept that used to express the relationship between the variables in easy manner . The following are the some properties of the log functions.

Graph:

The graphical representation that used to express the function is known as graph. The graph has x and y axis.  Let see some problems on inverse log graph.


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Example Problem on Inverse Log Graph :

In this article we are going to see some problems on inverse log graph and some practice problems for testing your inverse log graph skills.

Problem 1:

Find the inverse of the log function f(x) = log 7x and draw the graph

Solution :

Given f(x) = log 7x

We need to find the inverse of the given function.

To find the inverse of the given function, taking exponent on both side,

Before that substitute f(x) = y

y = log 7x

e^y = e^(log 7x)

We know that e^logx = x

e^y = 7x

Divided by 7 on both sides,

(e^y)/7 = (3x)/7

(e^y)/7 = x

x = (e^y)/7

Replace x = f^(-1)(x) and y = x

f^(-1)(x) = (e^x)/ 7

 The inverse of the given function is f^(-1)(x) = (e^x)/7

 y = e^x/7

Substitute x = -2, -1, 0, 1, 2 and get y value for draw the graph,

y = e^(-2) / 7 = 0.0193    ≈ 0.01

y = e^(-1) / 7 = 0.052      ≈  0.05

y = e^(0) / 7  =  0.142       ≈ 0.10

y = e^(1) / 7 =  0.388       ≈  0.4

y = e^(2) / 7 = 1.055         ≈ 1.1

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Practice Problem on Inverse Log Graph :

Problem :

Find the inverse of  a logarithms function f(x) = log 11xand draw the graph.

Solution

The inverse of the given function is f^(-1)(x) = e^(x) /11