Question

if a=log 3 5 and b=log 17 25 then which one is greater

Answer 1

Given: a=log (base = 3) 5 and b=log (base =17) 25

To find: Which one is greater?

Solution:

• Now we have given a=log (base = 3) 5 and b=log (base =17) 25

• Now we can observe that we can write 25 as 5² in b, so:

            a=log (base = 3) 5 and b=log (base =17) 5²

• We know that log(base=a)b = 1 / log(base=b)a

• Now reciprocating both we get:

            a=1 / log (base = 5) 3 and b=1 / log (base =5²) 17

• From b taking exponent out, we get:

            a=1 / log (base = 5) 3 and b=1 /1/2 x  log (base =5) 17

            a=1 / log (base = 5) 3 and b=2 / log (base =5) 17

• Now let

            log (base = 5) 3 = 1/x and 1/2 log (base =5) 17 = 1 / y

            log (base = 5) 3 = 1/x and log (base =5) √17 = 1 / y

            Now from above we can say that √17 > 3

            so log (base =5) √17 > log (base = 5) 3

• So,

            b=log (base =17) 25 > a=log (base = 3) 5

Answer:

            b=log (base =17) 25 > a=log (base = 3) 5