log(log x)=4

Question

It is supposed to be solved without a calculator! Please help! I am so confused. I thought the answer would be 10,000 (10^4), but it is not correct. 

Answer 1

Well... 10,000 cannot be right. In fact,

 

log(log(10,000) = log(4) .

 

Think of it like this:

 

10^log(log(x)) = 10⁴

 

which is the same as:

 

log(x) = 10⁴

 

And therefore x = 10^10⁴ which is a huge number:  10¹⁰⁰⁰⁰