If $$25^{3.8}×5^{4.2}÷5^{6.4}=25^x$$​, then the value of $$x$$​ is:

Correct option is A

Given:

​$$25^{3.8} \times 5^{4.2} \div 5^{6.4} = 25^x$$​​

Formula Used:

​$$a^m \times a^n = a^{m+n}$$​​

​$$a^m \div a^n = a^{m-n}$$​​

Solution:

​$$5^{7.6} \times 5^{4.2} \div 5^{6.4} = 5^{2x}$$​​

​$$5^{7.6 + 4.2 - 6.4} = 5^{2x}$$​​

​$$5^{5.4} = 5^{2x}$$​​

Since the bases are the same, equate the exponents:

5.4 = 2x

​$$x = \frac{5.4}{2} = 2.7$$​