Prove
`log_(b)b = 1`

Prove log_(b) 1=0

Prove log_(x)b^(x)=x

Prove: x^(log(b/c) ) x^(log((c)/(a))) x^(log((a)/(b)))=1

Prove that log_(e)(1+x)ltxforxgt0

Prove that log_(7) log_(7)sqrt(7sqrt((7sqrt7))) = 1-3 log_(7) 2 .

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

Prove that log_(4)2-log_(8)2+log_(6)2..."is"1-log_(e)2.

Prove that log 2 + 16 "log"16/15 + 12 "log" 25/24 + 7 "log" 81/80 = 1

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) .

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