Question

What are the values of a, b, and c if 2^a*3^b*5^c=2250?Please answer it with process.

Answer 1

${2}^{3a} \times {3}^{5b} \: \times {5}^{c} = \: 2250$

${2}^{3a} \times {3}^{5b} \: \times {5}^{c} = \: {2}^{1} \times {3}^{2} \times {5}^{3}$

[ By Prime factorisation of 2250]

On comparing ,

$a \: = \frac{1}{3} \\ \: b = \frac{2}{5} \\ \: c = \frac{3}{1}$