Express M in terms of N:
`log_(10)N=3 -2 log_(10)M`

Express M in terms of N: 1/2 log_(3) M +log_(3)N=1

Express log_(10)2 + 1 in the form of log_(10)x .

Express log_(10) root(5)(108) in term of log_(10)2 and log_(10)3 .

Given log_(2)x = m and log_(5) y = n (i) Express 2^(m-3) in terms of x. (ii) Express 5^(3n + 2) in terms of y.

Given : log_(3) m = x and log_(3) n = y (i) Express 3^(2x - 3) in terms of m. (ii) Write down 3^(1 - 2y + 3x) in terms of m and n. (iii) If 2 log_(3) A = 5x - 3y , find A in terms of m and n.

if (1+3+5-...upto n terms)/(4+7+10+...upto n terms)=20/(7log_10 X and n = log_10 x + log_10 X^1/2 + log_10 X^1/4 + ............ + oo , then x is equal to

If (1 + 3 + 5 + .... " upto n terms ")/(4 + 7 + 10 + ... " upto n terms") = (20)/(7 " log"_(10)x) and n = log_(10)x + log_(10) x^((1)/(2)) + log_(10) x^((1)/(4)) + log_(10) x^((1)/(8)) + ... + oo , then x is equal to

If (1 + 3 + 5 + .... " upto n terms ")/(4 + 7 + 10 + ... " upto n terms") = (20)/(7 " log"_(10)x) and n = log_(10)x + log_(10) x^((1)/(2)) + log_(10) x^((1)/(4)) + log_(10) x^((1)/(8)) + ... + oo , then x is equal to

The least positive integral value of the expression (1)/(2) log_(10) m - log_(m^(-2)) 10 is ______.

Write the following expressions as log N and find their values. log 10 + 2 log 3 - log 2