Would appreciate some guidance on the problem below:

Solve Log[base 25](6x + 25) + Log[base 5](x + 25) = 5, x a Natural number

To solve I tried converting to a single base using Log[base A]x = Log[base B]x / Log[base B]A which gives:

Log[base 25](6x + 25) = Log[base 5](6x + 25) / Log[base 5]25 = Log[base 5](6x+25) / 2

So the equation becomes:

Log[base 5](6x + 25) / 2 + Log[base 5](x + 25) = 5

Log[base 5](6x + 25) + 2Log[base 5](x + 25) = 10

Log[base 5](6x + 25) + Log[base 5](x + 25)^2 = 10

Log[base 5](6x + 25)(x + 25)^2 = 10

5^10 = (6x +25)(x +25)^2

This seems like a nasty polynomial to solve - is there a simpler approach to the problem?

Thanks in advance

Corbomite1