Logarithm of Complex Number

Introduction to logarithm of complex number:


In this article we will study about logarithm of complex number. In this foundation is the higher grade mathematics. Logarithm is used to solve many complex problems in easy way. In this content we are going to discuss about logarithm of complex number. The following are the examples involved in logarithm of complex number

Sample Problem for Logarithm of Complex Number:

Logarithm of complex number Problem 1:

Solve the given logarithmic expression: in 3x + in 5 = 3

Solution:                                                                                                                            

Given logarithmic expression: ln 3x + ln 5 = 3

in 3x + 1.6094 = 3                   ( The value of ln 5 = 1.6094)

Subtract by 1.6094 on both side in the above expression.

ln 3x + 1.6094 - 1.6094 = 3 - 1.6094

ln 3x =  1.3906   

log e 3x = 1.3906                        (ln x = loge x)        

(We know, y = logbP       and P = by)

Here, y = 1.3906         P = 3x                b = e

So,    3x = e1.3906   = 4.0172

3x = 4.0172

Divided by 3 on both side in the above equation

=3x/3 = 4.0172/3

x = 1.3390

Answer: The value of x = 1.3390

Logarithm of complex number Problem 2:

Solve the problems `log 10^x = log^5`

Solution:

Step i: given  ` log 10^x = log^5`

Step ii:  simplify the equation using with law (when the log base to the power here we can written like multiplication of log term)

` x.log10=log^5`

Step iii: evaluate for x, here we can dividing each side by log10



`x = (log^5/log10)`

`x = (log^5/log10)`

Or

Step iv: Take log value for the terms

Log 5= 0.69900

Log 10=1

` x =0.69900/1`

Step v: x = 0.699.

Logarithm of complex number Problem 3:

Solve the problems 61 log29+61 log27 = 66 log2 (7x)

Solution:

Logarithmic function 61 log25+61 log27=61 log2 (7x)

61 log2(9*7)  =61 log2(7x)

log2(63)=log2(7x)  by logarithm rules

Equate both sides, s the base are same 2, 7x = 63

Simplification: `x =63/7`

Answer = 9

Algebra is widely used in day to day activities watch out for my forthcoming post on algebraic expressions  I am sure they will be helpful.

Practice Problem for Logarithm of Complex Number:

Get the values of given problems `log^8 + log^4 + log^5`
Answer:log (160)

2. Solve the given logarithmic expression: In 6x + In 5 = 6

Answer: x = 0.163390