Solution-
1-
[tex]\Rightarrow 3^{\square}=27^{2x}[/tex]
[tex]\Rightarrow 3^{\square} = (3^{3})^{2x} = 3^{6x}[/tex] (∵ If the bases in both exponentials are same, then the powers are also equal )
[tex]\Rightarrow \square = 6x[/tex]
2-
[tex]\Rightarrow 25^{\frac{3}{2}} =5^{\square}[/tex]
[tex]\Rightarrow (5^{2})^{\frac{3}{2}} =5^{\square}[/tex]
[tex]\Rightarrow 5^{3} =5^{\square}[/tex]
[tex]\Rightarrow \square=3[/tex]
3-
[tex]\Rightarrow 4.253^{2t}=\square^{t}[/tex]
[tex]\Rightarrow (4.253^2)^{t}=\square^{t}[/tex]
[tex]\Rightarrow (18.08)^{t}=\square^{t}[/tex]
[tex]\Rightarrow \square=18.08[/tex] (∵ If the powers in both exponentials are same, then the bases are also equal )
