`3^[log_3logsqrtx]-logx+log^2x-3=0`

Match the column Column I, Column II If x=3,t h e n(log)_4(2(log)_3(1+(log)_2(1+3Log_3x))) is equal to, p. 3 If x=100 , then 3^((log)_3logsqrt(x))-logx+log^2x is equal to, q. 1 If one of the root of the equation 2((log)_xsqrt(5))^2-3(log)_x(a)+1=0 is sqrt(5) , then the other root is, r. 1/2 If (log)_2(4. 3^x-6)-(log)_2(9^x-6)=1, then x is equal to, s. 5

3^(log_(3)log sqrt(x))-log x+(log x)^(2)-3=0

Solve the following equation : log_x 2+log_x 4+log_x 8+log_x 16=10

solve for x if log_(4)log_(3)log_(2)x=0 and log_(e)log_(5)(sqrt(2x+2)-3)=0

Solve for x: a) (log_(10)(x-3))/(log_(10)(x^(2)-21)) = 1/2 b) log(log x)+log(logx^(3)-2)= 0, where base of log is 10. c) log_(x)2. log_(2x)2 = log_(4x)2 d) 5^(logx)+5x^(log5)=3(a gt 0), where base of log is 3. e) If 9^(1+logx)-3^(1+logx)-210=0 , where base of log is 3.

Prove that the value of each the following determinants is zero: |[logx,logy,logz],[ log2x ,log2y ,log2z ],[log3x, log3y ,log3z]|

Prove that the value of each the following determinants is zero: |[logx,logy,logz],[ log2x ,log2y ,log2z ],[log3x, log3y ,log3z]|

Show that |(log x, log y, logz),(log 2x, log2y, log2z),(log3x, log3y,log3z)|=0

Solve (log_(3)x)(log_(5)9)- log_x 25 + log_(3) 2 = log_(3) 54 .

Solve (log_(3)x)(log_(5)9)- log_x 25 + log_(3) 2 = log_(3) 54 .