Logarithm

First let's understand what Logarithm of a number is. The log of a number is the exponent or power or index to which the base of that number must be raised  to give you the number in question.

Example:

log1000 to base 10=3

When a log of a number is written without a base, its base is 10. Remember, we said that, the log of a number is the exponent or power or index of its base which will give the number in question. In this case the number is 1000 to base 10. So, the power to which 10 must be raised to give 1000 is 3. Therefore, the log of 1000 to base 10 is 3.

Expect more on Logarithm.

Expressing exponential numbers in Logarithm:

Having understood the meaning of logarithm, it is easy to express numbers in Index form  in Logarithm.

Example:

Express 8²=64  in Logarithmic form.

                  Solution:

8²=64 

In the given number above, 8 is known as the base while 2 is the Index or exponent or power. The 2 is the Logarithm of 64 to base 8 and it is written as:

Standard form(Scientific notation)

Standard form is a number of the form, A×10^n

Where A is between 1 and 10, i.e, 1 2 3 4 5 6 7 8 9 while n is the number of places the decimal point is moved to the left or right.
When the decimal point is moved to the left, n is positive while it is negative when moved to the right.
When a whole number is written, it has its decimal point at the end.
E.g write in standard form 2567653
Solution:
2567653
To make this number fall between 1 and 10, the decimal point has to be between 2 and 5, therefore, 2567653=2.567653×10^6.
Note that the exponent is positive because the decimal point is moved to the left.
Express in standard form, 0.025
Solution:
When expressing a decimal fraction in standard form, always moved the decimal point to the right such that the whole number is between 1 and 10 and the power must be negative in correspondence to the number of places the decimal point is moved to the right.
So, 0.025=2.5×10^-2

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  Please carefully study these for easier understanding of my next lesson. See you soon!  When expressing numbers in standard form or scientific notation, always remember that, when  the decimal point is moved to the right, the power or index or exponent must be negative  while if it is moved to the left, the power or Index or exponent must be positive. See example below: