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

Prove log_(b)b = 1

Prove log_(b) 1=0

If x,y,z are in G.P prove that log_(a)^(x)+log_(a)^(z)=(2)/(log_(y)^(a)),[x,y,a gt0]

Prove that log_(b^3)a xx log_(c^3)b xx log_(a^3)c = 1/27

Prove that log_(a)bxxlog_(b)cxxlog_(c )a=1

Prove that log_(1/y)x xx log_(1/z)yxx log_(1/x)z=-1

If f(x)=5^x , then prove : f(log_5x)=x

If log_(p)x=a and log_(q)x=b prove that log_(p/q)x=(ab)/(a-b)

Prove that /_\ log f(x) = log[ 1+ (/_\ f(x))/(f(x) ].

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) .