If `a= b^(1//3)=c^(1//5)=d^(1//7)=e^(1//9)` find `log_(a) abcde`.

If a=b^(2)=c^(3)=d^(4), then the value of log_(a)(abcd) would be a.(log_(a)1+(log)_(a)2+(log)_(a)3+(log)_(a)4b(log)_(a)24c.1+(1)/(2)+(1)/(3)+(1)/(4)d1+(1)/(2!)+(1)/(3!)+(1)/(4!)

Given a=1(5)/(7),b=(1)/(4),c=(1)/(9) and d=-1(1)/(4), then the value of (a(b-c))/(d) is

If (3)/(4)+(1)/(3)((3)/(4))^(3)+(1)/(5)((3)/(4))^(5)+....=log_(e)a,(1)/(3)+(1)/(3.3^(3))+(1)/(5.3^(5))+(1)/(7.3^(7))+....=log_(e)b, 1+(1)/(3.2^(2))+(1)/(5.2^(4))+(1)/(7.2^(6))+....=log_(e)c then the ascending order of a, b, c is

Find the value of (i) (log_(10)5)(log_(10)20)+(log_(10)2)^(2) (ii) root3(5^((1)/(log_(7)5))+(1)/((-log_(10)0.1))) (iii) log_(0.75)log_(2)sqrtsqrt((1)/(0.125)) (iv)5^(log_(sqrt(5))2)+9^(log_(3)7)-8^(log_(2)5) (v)((1)/(49))^(1+log_(7)2)+5^(-log_(1//5)7) (vi) 7^(log_(3)5)+3^(log_(5)7)-5^(log_(3)7)-7^(log_(5)3)

if (a)/(b)=(c)/(d)=(e)/(f)=(1)/(3) , then (5a+3c+7e)/(5b+3d+7f)= _________

If A=[{:(1,5),(7,12):}],B=[{:(9,1),(7,8):}] find a matrix C such that 3A+5B+2C is a null matrix.