Question

Find the value of-
log 4 to the base 5 × log 5 to the base 2​

Answer 1

Answer:

Let x = log base5 4 which means 5^x = 4… (1)

Let y = log base2 5 which means 2^y = 5…. (2)

We have to find log base5 4 * log base2 5 i.e. we have to find x * y

From (1), 5^x = 4 means 5 = 4^(1/x) =2^(2/x) .. (3)

Comparing (2) and (3) we get 2^y = 2^(2/x) i.e. y = 2/x or x * y = 2 which is the required product

Step-by-step explanation:

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