 # Checking a math problem

I think I did this correctly.

If a google = (x)^5^10 what is the value of x.

What I get is x^50 = 10^100.
10^2^50 = 10^100
Therefore the answer is 10 squared or 100.

Darn, I had totally forgotten that a googol and google are not spelled the same.

if a[sup]b[/sup] = c then a = c [sup]1/b[/sup]

10[sup]100[/sup] = x[sup]5[sup]10[/sup][/sup]
10[sup]100[/sup] * [sup]1/10[/sup] = x[sup]5[/sup]
10[sup]10[/sup] = x[sup]5[/sup]
10[sup]10[/sup] * [sup]1/5[/sup] = x
10[sup]2[/sup] = x

Well? Which is it??

sorry

There’s some ambiguity in the problem since exponentiation is not associative.

I’m more accustomed to interpret a^b^c as a^(b^c), but I’m not entirely sure that that is really standard.

In that case, however, the answer would be 10^(0.00001024), which is slightly larger than 1.

Exponentiation is right-associative, which means that the way you have it is indeed the convention.

And that means that x^5^10 = x ^ 9,765,625.

10^(0.00001024) = 1.00002358

Which means that 1.00002358^9 765 625 = 1.01228821 × 10[sup]100[/sup]

A bit high. 1.00002357874937 is closer. 1.00000043 × 10[sup]100[/sup]