Question

if 3^a=5^b=75^c then the value of ab-c(2a+b) reduces to ?????????

Answer 1

Given: 3^a = 5^b = 75^c

To find: The value of ab-c(2a+b) reduces to ?

Solution:

• Now we have given 3^a = 5^b = 75^c.

• Consider  3^a = 5^b .............(i)

• Taking ln on both sides, we get:

              a ln 3  = b ln 5        ............(ii)

              ln 3 = b ln 5 / a  .............(iii)

• Consider 5^b = 75^c .............(iv)

• Taking ln on both sides, we get:

              b ln 5 = c ln 75

              b ln 5 = c ln (3x5^2)

              b ln 5 = c (ln 3 + ln 5^2)

              b ln 5 = c (ln 3 + 2 ln 5)    ..............(v)

• Putting iii in v, we get:

              b ln 5 = c ((b ln 5 / a) + 2 ln 5)

              ab ln 5 = bc ln 5  + 2ac ln 5

• cancelling ln 5 from both sides, we get:

              ab = bc + 2ac

              ab - bc - 2ac = 0

              ab - c(b + 2a) = 0

Answer:

          So the value of ab - c(b + 2a) is 0.

Answer 2

Answer:

ab - c (2a+b) = 0

Step-by-step explanation:

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