Question

The graph of the linear equation
Prove that logan" = nlog, m?
• Prove that lone​

Answer 1

Prove that: log(a)'m'^n = 'n'log(a)'m'

Proof:

Let 'x' = log(a)'m' ------(i)

=> (a)^x = m -----(ii) (a^m = b)

Now, (m)^n = ((a)^x)^n -----(From (ii))

=> m^n = a^(xn)

=> log(a)'m'^n = xn (lo

=> log(a)'m'^n = log(a)'m' x n ------(From (i))

=> log(a)'m'^n = 'n'log(a)'m'

Hence, proved.