Answer:
Step-by-step explanation:
We have the equation:
Let's simplify this a bit. Let . Then . We can substitute the exponents:
Use the properties of exponents, we can write . We can do the same thing on the right. So:
We can now factor out a from the left and a on the right. This yields:
Evaluate the expressions within the parentheses:
Evaluate:
Now, let's multiply both sides by . So:
Also, let's divide both sides by . Multiply on the right:
Therefore:
We can now substitute back u. Notice that 27 is the same as 3 cubed and 1000 is the same as 10 cubed. So:
Since they have the same base, their exponents must be equal. Therefore:
Add 2 to both sides:
So, the value of x is 5.
And we're done!