Evaluate the determinant `=|((log)_3 512,(log)_4 3),((log)_3 8,(log)_4 9)|` .

Solve (log)_4 8+(log)_4(x+3)-(log)_4(x-1)=2.

Find the value of ((log)_3 4)((log)_4 5)((log)_5 6)((log)_6 7)((log)_7 8)((log)_8 9)dot

Find the value of ((log)_3 4)((log)_4 5)((log)_5 6)((log)_6 7)((log)_7 8)((log)_8 9)dot

Find the value of ((log)_3 4)((log)_4 5)((log)_5 6)((log)_6 7)((log)_7 8)((log)_8 9)dot

|[(log)_3 512,(log)_4 3],[(log)_3 8,(log)_4 9]|xx|[(log)_2 3,(log)_8 3],[(log)_3 4,(log)_3 4]|= (a) 7 (b) 10 (c) 13 (d) 17

Comprehension 2 In comparison of two numbers, logarithm of smaller number is smaller, if base of the logarithm is greater than one. Logarithm of smaller number is larger, if base of logarithm is in between zero and one. For example log_2 4 is smaller than (log)_2 8\ a n d(log)_(1/2)4 is larger than (log)_(1/2)8. Identify the correct order: (log)_2 6 (log)_3 8> log_3 6>(log)_4 6 (log)_3 8>(log)_2 6> log_3 6>(log)_4 6 (log)_2 8<(log)_4 6

If 3^x=4^(x-1) , then x= (2(log)_3 2)/(2(log)_3 2-1) (b) 2/(2-(log)_2 3) 1/(1-(log)_4 3) (d) (2(log)_2 3)/(2(log)_2 3-1)

log_4log_5 25+log_3log_3 3

If a_1, a_2, a_3,....... are in G.P. then the value of determinant |(log(a_n), log(a_(n+1)), log(a_(n+2))), (log(a_(n+3)), log(a_(n+4)), log(a_(n+5))), (log(a_(n+6)), log(a_(n+7)), log(a_(n+8)))| equals (A) 0 (B) 1 (C) 2 (D) 3

Find the value of x satisfying the equation ((log)_3 root(3)(3x)+(log)_x root(3)(3x))dot(log)_3x^3+((log)_3 root(3)(x/3)+(log)_xroot(3)(3/x))dot(log)_3x^3=2