Prove
`log_(b)b = 1`

Prove log_(b) 1=0

Prove that log_(3) 81- 4 =0

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

Given a^2+b^2=c^2 . Prove that log_(b+c)a+log_(c-b)a=2 log_(c+b)a.log_(c-b)a,forallagt0,ane1 c-bgt0 , c+bgt0 c-bne1 , c+bne1 .

Prove that log_(10) 2" lies between " 1/4 and 1/3 .

Prove log_3(5) is irrational.

Prove that log_n(n+1)>log_(n+1)(n+2) for any natural number n > 1.

Prove that (log_(2)8)/(log_(3)9) =3/2

Prove that log_7 11 is greater than log_(8)5 .

Prove that asqrt(log_a b)-bsqrt(log_b a)=0