TITLE: Can you solve this exponential equation?
QUESTION [8 upvotes]: I'm supposed to solve the equation
$$3^x  + 3^\sqrt x = 90$$
What steps do I need in order to get the solution $x=4$?

REPLY [2 votes]: Another way is by inspection. Since the left hand side is sums of powers of 3, can we write 90 as the sum of powers of 3? 
Yes, $3^x+3^\sqrt{x}=90=81+9=3^4+3^2.$ 
Thus $x=4$.