If a=log1218, b=log2454 then the value of ab+5(a-b) is
1
We have
a=log1218=log218log212=1+2log232+log23 and
b=log2454=log254log224=1+3log233+log23.
Putting x=log23, we haveab+5(a−b)=1+2x2+x.1+3x3+x+(1+2x2+x−1+3x3+x)=6x2+5x+1+5(−x2+1)(x+2)(x+3)=x2+5x+6(x+2)(x+3)