common logs: 7^x+2<13^5-x

$$\\7^x+2<371293-x\\$$

 

$$7^x+2>2\qquad $always$$$

 

https://www.desmos.com/calculator/ufxzprl4v4

 

From the graph it can be seen that 

This statement is true if x>6.591   (approximately)