If $${{\text{7}}^x}{\text{ = }}\frac{1}{{343}}{\text{,}}$$   then the value of x is?

$$\eqalign{ & {{\text{7}}^x}{\text{ = }}\frac{1}{{343}} \cr & \Rightarrow {{\text{7}}^x}{\text{ = }}\frac{1}{{{7^3}}} \cr & \Rightarrow {{\text{7}}^x}{\text{ = }}{{\text{7}}^{ - 3}} \cr & \Rightarrow x = - 3 \cr} $$
(If bases are equal then their power are also equal)