# 6^x=22 How do i solve without a calculator?

I expanded log(base) 6 (22) to 6^x=22

How would I find x here? I know basically i gotta find the square root to whatever index will find what i need. but im lost

Yall didnt answer my question. Like yall ended up needing a calculator to get the approximate answer i wanna know whithout calculator

### 3 Answers

- DixonLv 72 months ago
You know that 6^1 = 6 and 6^2 = 36 so the answer will be between 1 and 2.

And since exponentials ramp up quickly at the end it will be nearer to 2.

Unless you go real old school and start remembering a few specific logs or learning hand calculation methods it would be hard to get more decimal places easily and quickly.

- ?Lv 72 months ago
You can work in any base (log). Lets use base 10. Apply Log each side to get

L(6^x) = L(22)

xL(6) = L(22)

x = L(22)/L(6) --> calculator.