Question

If 1125= 3^m*5^n. find m and n

Answer 1

Answer :- m= 2 and n = 3.

Explanation :-

Given :-

If 1125= 3^m*5^n. find m and n

$\begin{array}{r | l} 5 & 1125 \\ \cline{2-2} 5 & 225 \\ \cline{2-2} 5 & 45 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \end{array}$

LCM is :-

${5}^{3} \times {3}^{2}$

$1125 = {3}^{m} \times {5}^{n}$

On comparison :-

${3}^{m} \times {5}^{n} = {5}^{3} \times {3}^{2}$

Hence, m= 2 and n = 3.