Logarithm

In mathematics, the logarithm for a given number for a given base is the power or an exponent in which the base should be raised so as to create that number. For example, the logarithm or log of 10000 to base 10 is 4, because 4 is the power in which ten must be raised to produce 1000: 104 = 1000..

The logarithm of x to the base b can be written as log b(x) or, if the base is implicit, as log(x). So, for a number x, a base b and an exponent y,

If x = b y, then y = log b(x)
Laws of Logarithms:

While logarithm is just an exponent which is simply being written down on the following line.

Laws of logarithms
Example and Practice Problems on Logarithms to the Base 10:

Example 1:

Find the logarithm of 568 to base 10. Write this in the exponential form.

Solution:

Log 568 = 2.754

This indicates that102.754 = 5623

Mind investigation: 102 = 100 and 103 = 1000.

Our number 568 is between these two values, so it is reasonable.

Example 2:

Find the logarithm of 999 to base 10. Write this in the exponential form.

Solution:

Log 999 = 2.9999

This indicates that102.9999 = 5623

Mind investigation: 102 = 100 and 103 = 1000.

Our number 999 is between these two values, so it is reasonable.

My forthcoming post is on Markov Chains and Curve Fitting will give you more understanding about Algebra.

Example 3:

Find the logarithm of 8778 to base 10. Write this in the exponential form.

Solution:

Log 8778 = 3.943

This indicates that103.943 = 5623

Mind investigation: 103 = 1000 and 104 = 10000.

Our number 568 is between these two values, so it is reasonable.

Example 4:

Find the antilogarithm of the value -6.978

Solution:

This indicates that "if log N= -6.978, what is N?"

Using the laws of logarithm N = 10-6.978 = 0.000 000 105.

Practice problems:

Problem 1:

Find the logarithm of 4545 to base 10. Write this in the exponential form.

Solution:

The answer is 3.657.

Problem 2:

Find the logarithm of  555555 to base 10. Write this in the exponential form.

Solution:

The answer is 5.744.

Is this topic physics problems hard for you? Watch out for my coming posts.

Problem 3:

Find the logarithm of 8969 to base 10. Write this in the exponential form.

Solution:

The answer is 3.952.