If `log_(3)M=a_1+b_1` and `log_5M=a_2+b_2` where `a_1,a_2 in N` and `b_1,b_2 in [0,1)`. if `a_1a_2=6` then find the number of integral values of M.

If log_(3)M=a_(1)+b_(1) and log_(5)M=a_(2)+b_(2) where a_(1),a_(2)in N and b_(1),b_(2)in[0,1) .if a_(1)a_(2)=6 then find the number of integral values of M.

Let log_2N=a_1+b_1,log_3N=a_2+b_2 and log_5N=a_3+b_3 , where a_1,a_2,a_3notin1 and b_1,b_2 b_3notin [0,1) . If a_1=6,a_2=4 and a_3=3 ,the difference of largest and smallest integral values of N, is

Let log_2N=a_1+b_1,log_3N=a_2+b_2 and log_5N=a_3+b_3 , where a_1,a_2,a_3notin1 and b_1,b_2 b_3 in [0,1) . If a_1=6,a_2=4 and a_3=3 ,the difference of largest and smallest integral values of N, is

Let log_2N=a_1+b_1,log_3N=a_2+b_2 and log_5N=a_3+b_3 , where a_1,a_2,a_3notin1 and b_1,b_2 b_3 in [0,1) . If a_1=6,a_2=4 and a_3=3 ,the difference of largest and smallest integral values of N, is

Let log_2N=a_1+b_1,log_3N=a_2+b_2 and log_5N=a_3+b_3 , where a_1,a_2,a_3notin1 and b_1,b_2 b_3 in [0,1) . If a_1=6,a_2=4 and a_3=3 ,the difference of largest and smallest integral values of N, is

If the points (a_1, b_1),\ \ (a_2, b_2) and (a_1+a_2,\ b_1+b_2) are collinear, show that a_1b_2=a_2b_1 .

If the points (a_1, b_1),\ \ (a_2, b_2) and (a_1+a_2,\ b_1+b_2) are collinear, show that a_1b_2=a_2b_1 .

Show that two lines a_1 x+b_1 y+c_1=0 and a_2 x+b_2 y+c_2=0 . where b_1, b_2 ne 0 are: (i) Parallel if a_1/b_1=a_2/b_2 , and (ii) Perpendicular if a_1 a_2+b_1 b_2=0

Let a_1,a_2,a_3 ….and b_1 , b_2 , b_3 … be two geometric progressions with a_1= 2 sqrt(3) and b_1= 52/9 sqrt(3) If 3a_99b_99=104 then find the value of a_1 b_1+ a_2 b_2+…+a_nb_n