$$
10^{36} > 9^{37}
$$

$$
10^{36} > 9 * 9^{36}
$$

$$
\frac{10^{36}}{9^{36}}  > 9
$$

$$
(\frac{10}{9})^{36}  > 9
$$

$$
(1 + \frac{1}{9})^{36}  > 9
$$

$$
((1 + \frac{1}{9})^9)^4 > 9
$$

Applying [Bernoulli's inequality](https://en.wikipedia.org/wiki/Bernoulli's_inequality) $$(1+x)^r \geq 1+rx$$ to the inner term

$$
(1+\frac{1}{9})^9 \geq 1+9*\frac{1}{9}
$$

$$
(1+\frac{1}{9})^9 \geq 2
$$

Inserting into the outer term

$$
2^4 > 9
$$


Scroogey

I think it's $$10^{36} > 9^{37}$$,

Obviously, $$10^{36} > 9^{36}$$.

If you multiply the RHS by $$(10/9)^{36}$$ it will equal the LHS and that multiplier is greater than 9 (I'm pretty sure).



Undisciplined

Did not use a calculator, but used ChatGPT: 

![](https://m.stacker.news/68759)

SwapMarket

10^36 is bigger.

My approach is very childish like i imagined having stacks of 10, 36 layer higher. And stack of 9s , 37 layer higher.

I hope I'm not wrong lol

Imyourfed

Take heed, a characteristic single sat zap was just received. 
@Scroogey's neurons are on the case...

south_korea_ln

Wow, 5 different stackers zapped this post within 5 minutes of posting this...

Did I just hit the optimal posting time (9 AM CST)?

Evaluate, without using a calculator, which one is bigger:

Sats will be given for each different approach.

science

Evaluate, without using a calculator, which one is bigger:
$$
10^{36} \text{ or } 9^{37}\ ?
$$
Sats will be given for each different approach.

Previous iteration: https://stacker.news/items/815243/r/south_korea_ln (fun variant in https://stacker.news/items/815243/r/south_korea_ln?commentId=815534).
