Close Enough to Ramanujan's Favorite

Algebra Level 2

If 4 log ⁡ 12 ( x 9 ) + log ⁡ 12 ( x 6 ) = 126 4 \log_{12} \left(x^9\right) + \log_{12} \left(x^6\right) = 126 , find x . x.


The answer is 1728.

View wiki
Noel Lo by Noel Lo , 24, Singapore

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

6 solutions

Noel Lo
May 5, 2015

4 log ⁡ 12 x 9 + log ⁡ 12 x 6 = 126 4 \log_{12} x^9 + \log_{12} x^6 = 126

36 log ⁡ 12 x + 6 log ⁡ 12 x = 126 36 \log_{12} x + 6 \log_{12} x = 126

42 log ⁡ 12 x = 126 42 \log_{12} x = 126

log ⁡ 12 x = 3 \log_{12} x = 3

x = 1 2 3 = 1728 x = 12^3 =\boxed{1728}

49 Helpful 3 Interesting 0 Brilliant 0 Confused
Piyush Nanda
May 7, 2015

7 Helpful 0 Interesting 1 Brilliant 0 Confused

Moderator note:

Right. Bonus question: What does the title mean when it says "Close enough to Ramanujan's favourite"?

I think that Ramnujan's favorite number is 1729!

Hobart Pao - 6 years, 1 month ago

Dear Challenge Master, Ramanujan's favourite number is 1729. As you can see, many questions on Brilliant involve the number 1729. The answer to this question is 1728, just 1 less than 1729, hence the title!!

Noel Lo - 6 years, 1 month ago

Now only I know what's Ramanujan's number...

Hon Ming Rou - 5 years, 11 months ago

Both Noel and Piyush did the same, but why did Noel has a 6 times more upvotes. Still confused. Ha ha !!!! Just for fun!!!!

Prayas Rautray - 3 years, 11 months ago
Huzaifa Raghav
May 10, 2015

4log12 x^9 + log12x^6=126

36log12 x + 6log12x=126

42log12 x=126

log12 x= 3

x=12^3=1728

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Shaban Alshaba
May 6, 2015

4x9logx+ 6log x=42 log x =126 Log12 (x) =126/42 =3 3 X=12. =1728

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Paola Ramírez
May 6, 2015

4 log ⁡ 12 x 9 + log ⁡ 12 x 6 = 126 4 \log_{12} x^9 + \log_{12} x^6 = 126

36 log ⁡ 12 x + 6 log ⁡ 12 x = 126 36 \log_{12} x + 6 \log_{12} x = 126

42 log ⁡ 12 x = 126 42 \log_{12} x = 126

log ⁡ 12 x = 3 \log_{12} x = 3

x = 1 2 3 = 1728 x = 12^3 =\boxed{1728}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Exactly the same as mine haha!

Noel Lo - 6 years, 1 month ago
Kenneth Gibson
May 12, 2015

Ramanujan's favorite is 1729 = 10^3 + 9^3 = 1^3 + 12^3. 1728 = 10^3 + 9^3 - 1^3 = 12^3

0 Helpful 0 Interesting 0 Brilliant 0 Confused

wtf wtf wtf. Z.😠😠😠😠😠😠😠😠

Am Kemplin - 1 month, 2 weeks ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...