Question

if log 6 base 15=a,log 12 base 18=b,log 25 base 24=y then prove that y=5-b/2(ab+a-2b+1)

Answer 1

As log12(18)=a, we have 12a=18

i.e. (22×3)a=2×32

or 22a−1×3a−2=1

similarly as log24(54)=b, we have 24b=54

i.e. (23×3)b=2×33

or 23b−1×3b−3=1

Comparing the two 2a−1=3b−1 or 2a−3b=0 ........(A)

and a−2=b−3 or a−b+1=0 i.e. 2a−2b+2=0 ........(B)

Subtracting (A) from (B), we get

b+2=0 i.e. b=−2

and a=b−1=−3

hence ab+5(a−b)

=(−3)×(−2)+5×(−1)=6−5=1

(Note that (B) gives a−b=−1.)

Answer 2

Answer:

let assume

log 6 base 15 = alfa and

log 12 base 18 =beta

take the prime factors of 6,15,12,18,25,24

=2,3,5

I hope this will help you