Assuming that log (mn) = log m + logn prove that log `x^(n) = n log x, n in N`

Prove that : log _ y^(x) . log _z^(y) . log _a^(z) = log _a ^(x)

Prove by the principle of Mathematical Induction that log x^(n)=nlogx , for all n in N .

Prove that: log_a x=log_bx xx log_c b xx…xx log_n m xx log_a n

Prove that: log sin 8x = 3 log2+log sin x+ log cos 2x+log cos 4x

If y log x= x-y , prove that (dy)/(dx)= (log x)/((1+log x)^(2))

Evaluate : int x^n log x dx.

Given log x = m + n and log y = m - n, express the value of "log" (10 x)/(y^(2)) in terms of m and n.

Given log x = 2m - n, log y = n - 2m and log z = 3m - 2n, find in terms of m and n, the value of "log" (x^(2)y^(3))/(z^(4)) .

If log_(a)m = n , express a^(n-1) in terms of a and m.

If m = log 20 and n = log 25, find the value of x, so that : 2 log(x - 4) = 2m - n.