In the previous post we have discussed about Greatest Integer Function and In today's session we are going to discuss about How to tackle Logarithm Problem. The definition of the logarithm of a number x with respect to the base b is nothing but the exponent to which the base b has to be raised to get the number x. In other words, the logarithm of x to base b is the solution y of the equation.
by = x
The logarithm is denoted by logb. The conditions for a logarithm to be defined are: the base b must be a positive real number and must not equal to 1 and x must also be a positive number.
So we can see that the whole idea of logarithm is just to reverse the operation of exponentiation, which is nothing but raising a number to a power. For example, the third power or you can say cube of 3 is 27, because 27 is the product of three factors of 3:
by = x
It says that the logarithm of 27 with respect to the base 3 is 3.
If I tell you in a simple way then logarithm of any number is the exponent by which the base of the logarithm has to be raised to produce that number. For ex., the log of 100 to the base 10( which is the common logarithm) is 2, because 100 is 10 to the power 2:100 = 102 = 10 × 10.
So, if x = by, and we take log both side,
Then only y will remain on R.H.S because log is the reverse of exponentiation and b will go to the L.H.S as base of log(x) and written as y = logb(x), so log10(100) = 2.
The common logarithm, which is nothing but log with respect to base 10, has many applications in science and engineering.
We can reduce wide range quantities to smaller level by using logarithmic scales.
In order to get help in understanding the topics more: logarithm, average rate of change, you can just visit our next article. All this topics are well illustrated in CBSE Text Books.
by = x
The logarithm is denoted by logb. The conditions for a logarithm to be defined are: the base b must be a positive real number and must not equal to 1 and x must also be a positive number.
So we can see that the whole idea of logarithm is just to reverse the operation of exponentiation, which is nothing but raising a number to a power. For example, the third power or you can say cube of 3 is 27, because 27 is the product of three factors of 3:
by = x
It says that the logarithm of 27 with respect to the base 3 is 3.
If I tell you in a simple way then logarithm of any number is the exponent by which the base of the logarithm has to be raised to produce that number. For ex., the log of 100 to the base 10( which is the common logarithm) is 2, because 100 is 10 to the power 2:100 = 102 = 10 × 10.
So, if x = by, and we take log both side,
Then only y will remain on R.H.S because log is the reverse of exponentiation and b will go to the L.H.S as base of log(x) and written as y = logb(x), so log10(100) = 2.
The common logarithm, which is nothing but log with respect to base 10, has many applications in science and engineering.
We can reduce wide range quantities to smaller level by using logarithmic scales.
In order to get help in understanding the topics more: logarithm, average rate of change, you can just visit our next article. All this topics are well illustrated in CBSE Text Books.
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