IF a=log₂3 , b=log₂5, c=log₇2 , then find the value of log₁₄₀63 in terms of a,b,c?

hi abhishek 

log ₁₄₀ 63 = log₂ 63 / log₂ 140 =  log₂ ( 7 * 3² ) / log₂ ( 7 * 5 * 2² )      eqn 1  ---- property of log

and    3  =  2 ^ a           

5 = 2 ^ b    and    7 = 2 ^ (1/c)      ----- given information and definition of logarithm

putting the value in equation 1 

(log₂  7 + 3 * log₂  3) / (log₂ 7 + log₂  5 +  2 log₂ 2 ) 

put the values of  3 , 5 , 7 in terms of a , b , c

u will get     {(1/c) + 3a}   /  { (1/c) + b + 2 }