Verified answer

So I think that this is what you mean: log[sqrt(75+3sqrt(x-1))=1.

To solve this make both sides of the above equation the exponent of 10--this gives: sqrt(75+3sqrt(x-1))=10.

Now square both sides to get: 75+3sqrt(x-1)=100--subtract 75 from both sides to get: 3sqrt(x-1)=25. Now square both sides again to get:

9(x-1)=625---so 9x-9=625 which means that 9x=634 and finally this means that x=70.444444