Prove
`log_(b)b = 1`

Prove log_(b) 1=0

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

Prove log_3(5) is irrational.

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

Prove that (log)_7 10 is greater than (log)_(11)13.

Prove that ((log)_a N)/((log)_(a b)N)=1+(log)_a b

If a^2+b^2=23 a b , then prove that log((a+b))/5=1/2(loga+logb)dot

Given log_(10)2 = a and log_(10)3 = b . If 3^(x+2) = 45 , then the value of x in terms of a and b is-

Let log_(c)ab = x, log_(a)bc = y and log_(b) ca = z . Find the value of (xyz - x - y - z) .

Given a^2+b^2=c^2, a >0 ; b >0; c >0,\ c-b!=1,\ c+b!=1,\ prove that : (log)_("c"+"b")a+(log)_("c"-"b")a=2(log)_("c"+"b")adot(log)_("c"-"b")a