Question

do the question 13.picure enclosed

Answer 1

we know logarithm concept
log (a base b)=1/log (b base a)
use here this concept

1/(log5 x)(log4 x)+1/(log5 x)(log3 x)=1/(log3 x )(log4 x )(log5 x) -1/(log3 x )(log4 x)

let
log3 x=p
log4 x =q
log5 x=r

hence

1/qr+1/rp=1/pqr - 1/pq

1/qr +1/pq+1/pr=1/pqr

(p+q+r)/pqr= 1/pqr

p+q+r=1


hence
log3 x + log4 x + log 5 x=1

log60 x=1

x=60