Evaluate :
`log_a^1 + log_a^2 + log_a^3 = ?`

Evaluate log_2 log_2 log_3 81

Find the value of log m + log m^(2) + log m^(3) +……. + log m^(n) :

Evaluate (log9-log3+1/2log81)/(2log3)

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|

log_2 [log_3(log_2 x)]=1

If x = log_(3) 4 " and " y = log_(5) 3 , find the value of log_(3) 10 " and " log_(3) (1 . 2) in terms of x and y .

If log_(2) x xx log_(3) x = log_(2) x + log_(3) x , then find x .

Find the value of log_(5) log_(2)log_(3) log_(2) 512 .