If $${{\text{5}}^{\left( {x + 3} \right)}}{\text{ = 2}}{{\text{5}}^{(3x - 4)}}$$    then the value of x is = ?

Solution(By Examveda Team)

$$\eqalign{ & {{\text{5}}^{\left( {x + 3} \right)}}{\text{ = 2}}{{\text{5}}^{(3x - 4)}} \cr & \Rightarrow {{\text{5}}^{\left( {x + 3} \right)}}{\text{ = }}{\left( {{5^2}} \right)^{(3x - 4)}} \cr & \Rightarrow {{\text{5}}^{\left( {x + 3} \right)}}{\text{ = }}{{\text{5}}^2}^{(3x - 4)} \cr & \Rightarrow {{\text{5}}^{\left( {x + 3} \right)}}{\text{ = }}{{\text{5}}^{(6x - 8)}} \cr & \Rightarrow x + 3 = 6x - 8 \cr & \Rightarrow 5x = 11 \cr & \Rightarrow x = \frac{{11}}{5} \cr} $$