If `a^(2) + b^(2) = 7`ab, show that log`((a + b)/(3)) = (1)/(2)` (log a + log b ).

If a^(2)+b^(2)=23ab prove that log""(a+b)/5=1/2(loga+logb)

Prove that "log"_(a^(2))a " log"_(b^(2)) b" log_(c^(2))c = (1)/(8) .

Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

If log_(a) 3 = 2 and log_(b) 8 = 3," then prove that "log_(a) b= log_(3) 4 .

If y^2=x z and a^x=b^y=c^z , then prove that (log)_ab=(log)_bc

Prove log ( a^(2))/(ba) + log((b^(2))/(ab))=0

Prove log a + log a^(2) + "log" a^(3) +……..+ log a^(n) = (n (n + 1))/(2) log a

If (log)_a3=2 and (log)_b8=3 , then prove that (log)_a b=(log)_3 4.

Which of the following numbers are positive/negative? (a) (log)_2 7 (b) (log)_(0. 2)3 (c) (log)_(1//3)(1/5) (d) (log)_4 3 (e) (log)_2((log)_2 9)