Value of Log 100

What is the value of log 100?

The value of log 100 is 2. Let us see how.

We take the following steps to solve this question.

• Since no base is mentioned, we will take the base of this log function to be 10.
  So, log 100=log₁₀100
• We know that the square of 10 is 100, or in terms of mathematics, 102=100

So, we write the following: log₁₀100=log₁₀10²

• By the properties of logarithm, log₁₀x^a= a log₁₀x. In this way, we can write.
  log₁₀10²=2 log₁₀10
• By properties of logarithm, log_aa=1. So, the value of log₁₀10 is also 1.
  Thus, 2 log₁₀10 = 2 x 1=2.

Hence, we see that the value of log 100 is 2.