If you take a look at the last line of the solution, you see:

If you just plug x = 1 you will get:

(3^1)*(5^1)^7^((1+1)/)) = 3*5*7

3*5*7 = 3*5*6 is true statement (identity), follows x = 1 is the solution.

Also, if you can graph the left side and the right side of equation, you will see the solution as the interception of these 2 graphs:

Click here to see the graphing.