Question

If log5 base 3=x and log11 base 25 =y then find value of log (11/3) base 3 in terms of x and y​

Answer 1

Here is the required solution.

Answer 2

Concept

The properties of logarithm is as follows,

Log a base a =1

Log a base c + log c base b = log a base b

Log (a/b) base c = log a base c - log b base c

Log a^b base c = b log a base c

We will use these properties to solve the given expression.

Given

Log 5 base 3 = x

Log 11 base 25 = y

Find

We have to calculate the value of the log (11/3) base 3 in terms of x and y.

Solution

Since, log (11/3) base 3 = log 11 base 3 - log 3 base 3

= log 11 base 3 -1

= log 11 base 25 + log 25 base 3 -1

= log 11 base 25 + 5 log 5 base 3 -1

= y + 5x - 1

Hence the value of log (11/3) base 3 is  y + 5x - 1.

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