What is a logarithm? In mathematics, the logarithm to the base b of a positive number y is defined as follows:
If y = b^{x}, then log_{b} y = x
Read log_{b} y as " log base b of y "
Just like we saw in the lesson about exponential function, b is not equal to 1 and b is bigger than zero.
The exponent x in the exponential expression b^{x} is the logarithm in the equation log_{b} y = x
What is a logarithm in easy terms?
Keep in mind that whenever you are looking for the logarithm, you are looking for an exponent, or the number that tells how many times the base is multiplied.
For example, what is the logarithm in log_{5} 25 = 2?
2 is the logarithm of the expression log_{5} 25. And it means that the base or 5 must be multiplied by itself 2 times to get 25.
Common logarithm
A common logarithm is a logarithm that uses base 10. Therefore, the expression log_{b} y = x becomes log_{10} y = x
As a result, you are always looking for the number of times you multiply 10 to get y.
You can write the common logarithm as log_{10} y or as log y
Writing in logarithm form
Write 49 = 7^{2} in logarithm form
Write the definition
If y = b^{x}, then log_{b} y = x
Substitute
If 49 = 7^{2}, then log_{7} 49 = 2
The logarithmic form of 49 = 7^{2} is log_{7} 49 = 2
Write 1/8 = (1/2)^{3} in logarithm form
Write the definition
If y = b^{x}, then log_{b} y = x
Substitute
If 1/8 = (1/2)^{3}, then log_{1/2} 1/8 = 3
The logarithmic form of 1/8 = (1/2)^{3} is log_{1/2} 1/8 = 3
Mar 13, 19 11:50 AM
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