The log function or logarithm function is used to eliminate the exponential functions when the equation has exponential values. It is used in mathematical problems to simplify the equations. The logarithmic function is defined by
if logab = x, then ax = b.
x is the logarithm of a number ‘b.’
‘a’ is the base of the log function.
Note: The variable “a” must be any positive integer where it should not be equal to 1.
The classification of logarithmic functions are:
- Common Logarithmic Function – Base 10 log function
- Natural Logarithmic Function – Base e log function
If the base of the logarithmic function is other than 10 or e, convert it into either base e or base 10 using the base change rule.
How to calculate the value of Log 4?
Now, let us discuss how to find the value of log 4 using a common log function and natural log function.
Value of Log10 4
The log function of 4 to the base 10 is denoted by “log10 4”.
According to the definition of the logarithmic function,
Base, a = 10 and 10x = b
With the use of logarithm table, the value of log 4 to the base 10 is given by 0.6020
Log10 4 = 0.6020
Value of ln (4) or loge 4
The natural log function of 4 is denoted by “loge 4”. It is also known as the log function of 4 to the base e. The representation of the natural log of 4 is ln(4)
The value of loge 4 is equal to 1.386294
loge 4 = ln (4) = 1.386294
Solve log(2 ×4 ×6).
Given that, log(2 ×4 ×6).
Using the properties of the logarithm (log a + log b = log ab)
It can be written as,
log(2 ×4 ×6) = log 2 + log 4 + log 6 ….(1)
We know that,
Log 2 = 0.3010
Log 4 = 0.6020
Log 6 =0.7781
Now substitute the log values in (1), we get
log(2 ×4 ×6) = 0.3010+0.6020 + 0.7781
log(2 ×4 ×6) = 1.6811
Therefore, the value of log(2 ×4 ×6) is 1.6811
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