I think the answer for n=21

5^21*4^11=2*10^n
5^21*2^22=2*5^n*2^n
Threfore n must equal 21

I am not sure. Please let me know if you know the correct solution

I think the answer for n=21

5^21*4^11=2*10^n
5^21*2^22=2*5^n*2^n
Threfore n must equal 21

I am not sure. Please let me know if you know the correct solution

The only way to solve this one is to realize what the exponents really mean.

You can think of 5^21 as a list of 21 5's multiplied together.

4^11 = (2^2)^11 = 2^22 and you can think of this as a list of 22 2's multiplied together.

Instead of multiplying the all of the 5's and then all of the 2's, then multiplying their products together, you can match up a 5 and 2. Now instead of 21 5's and 22 2's, you have 21 10's and a 2 to multiply together. And, clearly, another way to write that would be 2 * 10^21

The answer is 21

I got 21 as well. The key in this one is to see that when you split 10^n the result is not 2 * 5^n but is 2^n * 5^n. Another mistake that could be made is to ignore the 2 and forget that it is 2^1, leaving a 1 behind.