Question Number 55284 by Mikael_Marshall last updated on 20/Feb/19
$$\mathrm{5}^{{x}−\mathrm{2}} −\mathrm{5}^{{x}} +\mathrm{5}^{{x}+\mathrm{1}} =\mathrm{505} \\ $$
Commented by Kunal12588 last updated on 20/Feb/19
$$\left(\mathrm{5}^{{x}} ×\mathrm{5}^{−\mathrm{2}} \right)−\mathrm{5}^{{x}} +\left(\mathrm{5}^{{x}} ×\mathrm{5}\right)=\mathrm{505} \\ $$$$\mathrm{5}^{{x}} \left(\mathrm{5}^{−\mathrm{2}} −\mathrm{1}+\mathrm{5}\right)=\mathrm{505} \\ $$$$\mathrm{5}^{{x}} \left(\frac{\mathrm{1}−\mathrm{25}+\mathrm{125}}{\mathrm{25}}\right)=\mathrm{505} \\ $$$$\mathrm{5}^{{x}} =\frac{\mathrm{505}}{\mathrm{101}}×\mathrm{25}=\mathrm{125}=\mathrm{5}^{\mathrm{3}} \\ $$$${x}=\mathrm{3} \\ $$