6^(2x) = 46656

Question

6^(2x) = 46656

radar · Answer

Solve for x.

anonymous · Answer

$$46656=6^6$$

anonymous · Answer

$$6^6=6^{2x}$$

anonymous · Answer

$$6=2x~~~~~~~~x=3$$

anonymous · Answer

You know how to solve those, ...  you know math better than me :)

radar · Answer

2X log 6 = log 46656
2X(0.77815=4.6689
1.5563x = 4.6689
x=3

anonymous · Answer

Well, either way, standard approach vs a little extra thinking ;)

radar · Answer

I was wondering how to get that exponent without using logs, I see that logs work.  How did you come by the 6^6=46656.  My calculator has a key labeled x^y, I was hoping I could use that.

radar · Answer

@student_basil what was the "extra thinking" process?

anonymous · Answer

I just thought of dividing that huge number by 6 and count each time I divide by 6... I saw so many problems that like this in algebra that shouldn't require the knowledge of logarithms to be solved...

anonymous · Answer

So it had to be that there is some other way...

radar · Answer

I see, sort of trial and trial lol.

anonymous · Answer

yeah :)

zepdrix · Answer

The left side is a base of 6, $\Large\rm 6^{2x}$
So you want to find out if the right side can be written as a base of 6 as well.
So just take the 6th root of that huge number :o

zepdrix · Answer

That's my thinking pattern at least :3

radar · Answer

O.K, thanks @zepdrix

anonymous · Answer

It was good problem to solve, and we had a bunch of good approaches! tnx @radar  and everyone else !

radar · Answer

I see now that using the x^y key that by entering 46656 then depressing the x^y key and entering (1/6) will let me know the 6th root of 46656.  Just doing some experiementing with a casio fx-300W calculator....Thanks all.

anonymous · Answer

You welcome !