Value of log 8| Definition, Value in Common Log and Natural Log

A logarithm is the inverse operation of exponentiation. It helps us find the power to which a base must be raised to obtain a given number. In other words, if we have the equation:

bx=y

Then, the logarithm base b of y is denoted as:

log_b(y) =x

Common Logarithm 10log₁₀

The most common form of logarithm is the base-10 logarithm, often denoted as 10log₁₀​. To find the value of log 8 in base 10, we follow these steps:

1. Recognize that 10log₁₀​ is the common logarithm.
2. Calculate log₁₀​(8) by finding the exponent to which 10 must be raised to obtain 8.
3. log₁₀​(8)= log₁₀​1(8) = log₁₀​(2³) (since 8=2³=23).
4. log₁₀​(8 =3⋅log₁₀​(2).
5. Using log tables or calculators, log₁₀(2) ≈ 0.301.
6. Therefore, log₁₀(8) ≈ 3⋅0.301= 0.903.

So, the value of log 8 in common logarithm (base 10) is approximately 0.903.

Natural Logarithm – ln

The natural logarithm, denoted as ln, uses the base e, which is a mathematical constant approximately equal to 2.71828. To find the value of log 8 in the natural logarithm, we follow these steps:

1. Recognize that ln represents the natural logarithm.
2. Calculate ln(8) by finding the exponent to which e must be raised to obtain 8.
3. ln(8) ≈ 2.079.

So, the value of log 8 in the natural logarithm is approximately 2.079.