Find `log_a x + log_(a^2) x^2 + log_(a^3) x^3 + ........+ log_(a^n) x^n =`

Find x if log_(2) log_(1//2) log_(3) x gt 0

If log_(4) x + log_(8)x^(2) + log_(16)x^(3) = (23)/(2) , then log_(x) 8 =

Find x if 3^(log_(a)x)+3.x^(log_(a)3)=2

1+log_e x+ (log_e x)^2/2!+(log_e x)^3/3!+...=

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

Solve for x: log_(4) log_(3) log_(2) x = 0 .

Find x, if log x^(3) - log 3x =2 log 2 + log 3 ,

Find x if 9^(1//log_(2)3) le log_(2) x le log_(8) 27

log_(2)(3-x)+log_(2)(1-x)=3