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

Question

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

Update:

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

Answer 1

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.

 

Answer 2

6ˣ = 22

x log 6 = log 22

       log 22    

x = --------- ≈ 1.725  ...................ANS

       log 6

Answer 3

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.