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
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 of the expression log_{5} 25 ?
2 is the logarithm of the expression log_{5} 25. Why? In the expression, we can see that the base is 5.
Therefore, ask yourself, "5 to the power of what is equal to 25?"
Since 5^{2} = 25, log_{5} 25 = 2.
What is the logarithm of the expression log_{2} 16 ?
Since 2 to the fourth power is equal to 16, log_{2} 16 = 4.
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
What is log_{10} 1000 ?
Since 10 to the third power = 1000, log_{10} 1000 = 3.
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
Jan 26, 23 11:44 AM
Jan 25, 23 05:54 AM