To solve this equation, we can start by dividing both sides of the equation by (12/39)^(x/24+1):

1 = ((47/42)^(x/24+1))/((12/39)^(x/24+1))

Next, simplify the right side of the equation by using the properties of exponents:

1 = (47/42)^(x/24+1) / (12/39)^(x/24+1)
1 = ((47/42)/(12/39))^(x/24+1)
1 = (47/42)(39/12)^(x/24+1)
1 = (47/42)(13/4)^(x/24+1)

Now, since 1 = 1^k for any non-zero k, we can rewrite 1 as (13/4)^0:

(13/4)^0 = (47/42)*(13/4)^(x/24+1)

Since any number raised to the power of 0 is equal to 1, we now have:

1 = (47/42)*(13/4)^(x/24+1)

To find the value of x, we can isolate x by dividing both sides by (47/42)*(13/4)^(x/24+1):

1 / ((47/42)*(13/4)^(x/24+1)) = 1

Now, we have an equation where x is in the exponent. Unfortunately, this equation does not have a simple solution as it involves complex calculations and potentially irrational solutions.