Umm...exponent/square root problem

Okay Im trying to find log 5^x =5*sq rt of 5. Thats log base 5 with exponent x equals 5 times the square root of five or, with a base of five, what exponent do I need to get 5 times the square root of 5? Now I know to solve for an exponent you take the natural logarithm of both sides and solve for x which is easy and I know that the square root is the same thing as a number raised to the 1/2 power but even though I know how to solve components of this problem I dont know how to solve the actual problem.

Okay let me try this:

Yes thats it, and I need to solve for x.