Difference between revisions of "AoPS Wiki:Problem of the Day/September 16, 2011"
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When the equation | When the equation | ||
| − | <cmath>13^3x+13^x=10</cmath> | + | <cmath>13^{3x}+13^x=10</cmath> |
is solved for <math>x</math>, the result is <math>x=\log_{a}b</math>, where <math>a</math> and <math>b</math> are positive integers and <math>a</math> is not a multiple perfect power other than <math>1</math>. Find <math>(a+b)(a^2-ab+b^2)</math>. | is solved for <math>x</math>, the result is <math>x=\log_{a}b</math>, where <math>a</math> and <math>b</math> are positive integers and <math>a</math> is not a multiple perfect power other than <math>1</math>. Find <math>(a+b)(a^2-ab+b^2)</math>. | ||
<noinclude>[[Category: Problem of the Day]]<noinclude> | <noinclude>[[Category: Problem of the Day]]<noinclude> | ||
Latest revision as of 17:28, 16 September 2011
When the equation
![\[13^{3x}+13^x=10\]](http://latex.artofproblemsolving.com/e/e/7/ee7045029ba8640bc9c796c296792a0bbc6b338e.png)
is solved for 
, the result is 
, where 
and 
are positive integers and is not a multiple perfect power other than 
. Find 
.
