Harvard University Math Exam Tricks || Exponential Aptitude Test || How to Solve for x=?

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Harvard University Exam Question || Algebra Problem || Aptitude Simplification Test
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Пікірлер: 10
@2012tulio
@2012tulio Ай бұрын
Square both sides and let 5^x= a and 13^x= b and replace 65 by 5*13 and 169 by 13*13 you will get (a-b)^2 = ab-b^2 Expand and divide by b^2 you will get a quadratic equation (a/b)^2-3(a/b)+2=0 Solve for a/b Case 1: a/b = 2 Therefore (5/13)^x = 2 Taking log both sides you get x = -0.725 Case2 : a/b=1 Which means (5/13)^x= 1 X=0 X={0; -0.725}
@michaeldoerr5810
@michaeldoerr5810 Ай бұрын
Nice solution. And I shall use that for practice!!!
@superacademy247
@superacademy247 Ай бұрын
Go for it! Thanks
@RyanLewis-Johnson-wq6xs
@RyanLewis-Johnson-wq6xs Ай бұрын
x=-Log[2.6,2] x=-Log[13/5,2]
@YAWTon
@YAWTon Ай бұрын
Why this convoluted explanation? Once you have a=b or a=2b with a=5^x and b=13^x, the two solutions are obvious. Simply take the log of both sides and solve the linear equation in x.
@RyanLewis-Johnson-wq6xs
@RyanLewis-Johnson-wq6xs Ай бұрын
Log(2)/Log(5/13)=-Log(2)/Log(13/5)
@broytingaravsol
@broytingaravsol 29 күн бұрын
so easy
@prollysine
@prollysine 29 күн бұрын
x=ln2/ln(5/13) ,
@networkadministrator2736
@networkadministrator2736 Ай бұрын
Plz learn identities, and be fair
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