The strategy is to convert each side of the equation into multiples of 2 and 5 and then finallyequate.
\(10^{47}\) can be written as\((2.5)^{47}\)
Rewriting the equation asbelow:
\(\frac{(1)^m}{(5)^m}\) .\(\frac{(1)^{24}}{(4)^{24}}\) =\(\frac{1}{2.(2.5)^{47}}\)
\(4^{24}\) can be written as\((2^2)^{24}\) , which is equal to\(2^{48}\)
\(\frac{1}{(5)^m}\) .\(\frac{1}{(2)^{48}}\) =\(\frac{1}{2.(2.5)^{47}}\)
Now, cross multiply the denominators on both the sides.
\(2.(2.5)^{47}\) =\(5^m\) .\( 2^{48}\)
...
\(10^{47}\) can be written as\((2.5)^{47}\)
Rewriting the equation asbelow:
\(\frac{(1)^m}{(5)^m}\) .\(\frac{(1)^{24}}{(4)^{24}}\) =\(\frac{1}{2.(2.5)^{47}}\)
\(4^{24}\) can be written as\((2^2)^{24}\) , which is equal to\(2^{48}\)
\(\frac{1}{(5)^m}\) .\(\frac{1}{(2)^{48}}\) =\(\frac{1}{2.(2.5)^{47}}\)
Now, cross multiply the denominators on both the sides.
\(2.(2.5)^{47}\) =\(5^m\) .\( 2^{48}\)
...
