Can you solve below mathematical equation?

2^1234 - 2^1233

If 21x = 79x, what is the value of x?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

Which is the smallest number that you can write using all the vowels exactly once?

The more you take me, the more you leave me behind.
Who Am I?

Mother's Name is Mrs. SIXTY TWO
Son's Name is FIFTY TWO
Daughter's Name is FORTY TWO
What is Name of Father?

Astrology starts with the alphabet A, Biology starts with B, Psychology with P and Limnology with L.

Can you find an "ology" that begins with a P?

What do you call a fish without an eye?

You are given four results as below:
1111 = F
2222 = E
3333 = T
Then, can you find out how to code 4444?

You are mixing a mixture of cement and Sand with five gallons of water. You have a garden hose giving you all the water you need. The problem is that you only have a four-gallon bucket and a seven-gallon bucket and neither has graduation marks. Find a method to measure five gallons.