Show that :
`( loga )^2 -( logb )^2 = log(ab ) . log( a/b ) `

Show that the progression loga, log(ab) , log(ab^(2)),log(ab^(3)), …. is an AP. Find its general term and the 10th term.

Show that: |log_(b)a+log_(a)b|>=2

Show that the sequence log a,log(ab),log(ab^(2)),log(ab^(3)),... is an A.P.Find the nth term.

Show that the sequence log a,log(ab),log(ab^(2)),log(ab^(3)),... is an A.P.Find its nth term.

If f(x) = x (1 - log x), " where " x gt 0 , show that (a -b) log c = b (1 - logb) - a(1 - log a), " where " 0 lt a lt c lt b

If (a^(log_b x))^2-5 a^(log_b x)+6=0, where a >0, b >0 & a b!=1, then the value of x can be equal to (a) 2^(log_b a) (b) 3^(log_a b) (c) b^(log_a2) (d) a^(log_b3)

if a^(3-x)b^(5x)=a^(x+5)b^(3x), then the value of x log((b)/(a)) is : b (i) loga (ii) logb (iii) logx (iv) 1

4.Prove that log_(a)(bc).log_(b)(ca).log_(c)(ab)=2+log_(a)(bc)+log_(b)(ca)+log_(c)(ab)