Evaluate: `log_(a^2) b-:log_sqrt(a)(b)^2`

Evaluate log_2sqrt6+log_2 sqrt(2/3)

Express the following in exponential form: a) log_(2)32=5 b) log_(sqrt(2))4=4 c) log_(10)0.01=-2

Let A denotes the value of log_(10){(ab+sqrt((ab)^(2)-4(a+b)))/(2)}+log_(10){(log_(10)(ab-sqrt((ab)^(2)-4(a+b))))/(2)} and B denotes the value of the expression (2^(log_(6)18)) Find the value of (A*B)

The minimum value of 'c' such that log_(b)(a^(log_(2)b))=log_(a)(b^(log_(2)b)) and log_(a) (c-(b-a)^(2))=3 , where a, b in N is :

Find the value of log_(4)*log_(2)log sqrt(2)log_(3)(x-21)=0

the value of log_(a-b)(a^(3)-b^(3))-log_(a-b)(a^(2) +ab + b^(2)) is ______ . (a gt b)

The sum of the series log_(a)b+log_(a^(2))b^(2)+log_(a^(3))b^(3)+....log_(a^(n))b^(n)

The value of (6 a^(log_(e)b)(log_(a^(2))b)(log_(b^(2))a))/(e^(log_(e)a*log_(e)b)) is