If log 27 = 1.431, then the value of log 9 is ?

Step-by-Step Solution

To find the value of log(9) given log(27) = 1.431, we can relate both numbers to the base 3.

1. Understand the relationships:

   • 27 = 3^3

   • 9 = 3^2

2. Apply the Power Rule: The power rule states that log(x^y) = y * log(x).

   • Given log(27) = 1.431

   • log(3^3) = 1.431

   • 3 * log(3) = 1.431

   • log(3) = 1.431 / 3 = 0.477

3. Calculate log(9):

   • log(9) = log(3^2)

   • Using the power rule: log(9) = 2 * log(3)

   • log(9) = 2 * 0.477 = 0.954