Properties of logarithmic function Property `(5) log_a (x^n)=nlog_a|x| (6) log_a^n x^m=m/n log_a x (7) x^(log_a y)=y^(log_a x)`

Properties of logarithmic function Property (1) log_a 1=0 (2) log_a a=1 (3) log_a (xy)=log_a|x|+log_a|y| (4) log_a(x/y)=log_a |x|-log_a |y|

Properties of logarithmic function Property (8) If a>1 then the values of f(x)=log_a x increases with an increase in x ie xlty hArr log_a x lt log_a y (9) If 0

y = (log x) ^ ((log x) ^ (log x) .... oo)

log(x)^(n)=n.log x is true for

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 m^(log_(a)x)=x^(log_(a)m)

if log (x+y) = log x + log y , then x= ____

y = log_a^x , dy/dx