How would you write e^(10^23) in the form of 10^x for any x?

Answer 1

To do this, let's just solve for x for the following equation. This will give us the value of x, as well as the form.

e^(10^23) = 10^x

To solve for x, we convert this to logarithmic form.

log(e^(10^23)) = x

Moving 10^23 in front of the log, we get

[10^(23)] log(e) = x

Therefore

e^(10^23) = 10^ [ [10^(23)] log(e) ]

Answer 2

I solved a more general form. I've omitted some details:

Let
e^(10^y) = 10^x , now we want to find x in terms of y:

e^(10^y) = e^(x*ln(10))
10^y = x*ln(10)
x = 10^y/ln(10)