Question

4. Log81 ~ 25 is ( )
O Log 3 + log 5
O 3 + 5
3 lig 3 + 5 log 5
O Log 3 + 5 log 5
4 log 3 + 2 log 5
2 5​

Answer 1

Correct Question :-

Find the value of log₂₅81

Solution :-

By simplifying the given question ,

Here ,

• 81 can be written as 9²
• 25 can be written as 5²

Substituting we have ,

⇒ log_{5^2} ( 9² )

Using ,

• log_{aⁿ} ( bⁿ ) = logₐ(b)

Similarly ,

⇒ log₅ [ 9 ]

Substituting 9 = 3²

⇒ log₅ [ 3² ]

Using ,

• log [ aⁿ ] = n log(a)

⇒ log₂₅81 = 2 log₅(3)

Hence , log₂₅81 = 2 log₅(3)