# Solve For n

• MHB
mathland

I say we take the log on both sides as step one.

Yes?

Gold Member
MHB
log base 7 looks good, yes.

-Dan

HOI
The first thing I would do is start dividing 343 by 7! 343- 40(7)= 343- 280= 63= 9(7) so $$\displaystyle 343= 7(49)= 7(7)(7)= 7^3$$. $$\displaystyle \sqrt{343}= 7^{3/2}$$ so $$\displaystyle 7^{2n}= 7^{3/2}$$ so $$\displaystyle 2n= 3/2$$, n= 3/4.

No logarithms necessary!

mathland
The first thing I would do is start dividing 343 by 7! 343- 40(7)= 343- 280= 63= 9(7) so $$\displaystyle 343= 7(49)= 7(7)(7)= 7^3$$. $$\displaystyle \sqrt{343}= 7^{3/2}$$ so $$\displaystyle 7^{2n}= 7^{3/2}$$ so $$\displaystyle 2n= 3/2$$, n= 3/4.

No logarithms necessary!

Nicely done! It pays to know math tricks.

jonah1
Beer soaked non sequitur ramblings follow.
Nicely done! It pays to know math tricks.
A man's mind stretched by a new idea can never go back to its original dimension.

HOI
I don't think I would consider factoring a "trick".

mathland
I don't think I would consider factoring a "trick".

I meant to say skill not trick.