If `log_(2x) 20 sqrt6=log_(3x) 90,` then characteristic of `log_5 x^3` is equal to

If log_(3x)45=log_(4x)40sqrt(3) then find the characteristic of x^(3) to the base 7.

If N= anti log _(3)(log_(6)(antilog_(sqrt(5))(log_(5)(1296))) then the characteristic of log N to the base 2 is equal to

log_(x)2x<=sqrt(log_(x)(2x^(3)))

Let x=(((81^(1/( (log_(5)9))+3^(3/( log_(sqrt6)3)))/(409)).( (sqrt7)^((2)/(log_(25)7))-125^( log_(25)6))) then value of log_(2)x is equal to :

Let x=(((81^(1/( (log_(5)9))+3^(3/( log_(sqrt6)3)))/(409)).( (sqrt7)^((2)/(log_(25)7))-125^( log_(25)6))) then value of log_(2)x is equal to :

If log_(2)[log_(3)(log_(2)x)]=1 , then x is equal to

If x= log_(5)3 and y = log_(5)8 then log_(5)24 in terms of x,y is equal to _______

If f(x)=log_(5)log_(3)x , then f'(e ) is equal to