The value of log 125 base root 5 is equal to 6, that is, log√5125 = 6. In this post, we will learn how to find the logarithm of 125 when the base is √5.
How to Find log125 Base Root 5
Question: What is log125 base√5?
Answer: log125 base root 5 equals 6.
Solution:
Step 1:
We know that 125 is a product of three numbers of 5’s. In other words, we can write 125 as follows.
125 = 5×5×5
⇒ 125 = 53 …(∗)
Next, we write 5 as a power of √5.
5 = (√5)2
Thus, Equation (∗) can be rewritten as
125 = [(√5)2]3
∴ 125 = (√5)6 by the indices rule amn = (am)n
Step 2:
Now, we will take logarithms with base √5 on both sides. This will give us
log√5125 = log√5(√5)6
⇒ log√5125 = 6 log√5(√5)
⇒ log√5125 = 6, as we know the logarithm formula: logaa = 1.
Hence the value of log 125 base root 5 is 6.
Have You Read These Logarithms?
FAQs
Q1: What is log 125 with base root 5?
Answer: As 125=(√5)6, the value of the log125 with base root 5 is equal to 6.