can anyone give me his logarithm notes class 9?
Answers
A logarithm is defined as the power to which number must be raised to get some other values. It is the most convenient way to express large numbers. A logarithm has various important properties that prove multiplication and division of logarithms can also be written in the form of logarithm of addition and subtraction.
“The logarithm of a positive real number a with respect to base b, a positive real number not equal to 1[nb 1], is the exponent by which b must be raised to yield a”.
i.e by= a and it is read as “the logarithm of a to base b.”
Logarithm Properties
There are four basic rules of logarithms as given below:-
Logb (mn)= logb m + logb n. In this rule, the multiplication of two logarithmic values is equal to the addition of their individual logarithms.
For example- log3 ( 2y ) = log3 (2) + log3 (y)
Logb (m/n)= logb m – logb This is called as division rule. Here the division of two logarithmic values is equal to the difference of each logarithm.
For example, log3 ( 2/ y ) = log3 (2) -log3 (y)
Logb (mn) = n logb m
This is the exponential rule of logarithms. The logarithm of m with a rational exponent is equal to the exponent times its logarithm.
Logb m = loga m/ loga b
Logarithms problems
Question 1:
Solve log 2 (64) =?
Solution:
since 26= 2 * 2 * 2 * 2 * 2 * 2 = 64, 6 is the exponent value and log 2 (64)= 6.
Question 2:
What is the value of log10(100)
Solution:
In this case, 10 2 yields you 100. So, 2 is the exponent value, and the value of log10(100)= 2
Question 3:
Use of the property of logarithms, solve for the value of x for log3 x= log3 4+ log3 7
Solution:
By the addition rule, log3 4+ log3 7= log 3 (4 * 7 )
Log 3 ( 28 ). Thus, x= 28.
Question 4:
Solve for x in log 2 x = 5
Solution:
This logarithmic function can be written In the exponential form as 2 5 = x
Therefore, 2 5= 2 * 2 * 2 * 2 * 2 = 32, X= 32.
Logarithms Applications
Logarithms are nowadays widely used in the field of science and technology. We can even find logarithmic calculators which have made our calculations much easier. These find its applications in surveying and celestial navigation purposes. They are also used in calculations such as measuring the loudness (decibels), the intensity of the earthquake regarding Richter scale, in radioactive decay, to find the acidity (pH= -log10[H+]), etc.