Harvard University Admission Interview Problem || Algebra Aptitude Test || Entrance Exam || Find x=?

[@cdy4901]

X=sqrtX^sqrtX X²=X^sqrtX sqrtX=2=>X=4

[@BZKnowHow]

thumbs up

[@oahuhawaii2141]

You missed x = 1 .

[@jamesharmon4994]

At 1:28, I would realize the bases are the same and equate the exponents. x^1 = x^(sqrt(x)/2) therefore 1 = sqrt(x)/2. 2 = sqrt(x) x = 4.

[@oahuhawaii2141]

But you forgot that a base of 1 makes the exponents irrelevant. Thus, x = 1 is another solution.

[@Duc_Tung]

x = 1.

[@oahuhawaii2141]

You missed x = 4 .

[@oahuhawaii2141]

x = (√x)^(√x) x = x^(√x/2) log(x) = (√x/2)*log(x) log(x) - (√x/2)*log(x) = 0 log(x)*(1 - √x/2) = 0 log(x) = 0 , 1 = √x/2 x = 1 , x = 4

[@BZKnowHow]

great

[@arekkrolak6320]

You just wasted 0:25 time by writing the samr thing second time :)

[@BZKnowHow]

Noted sir I will take care of this next time....thank you for your feedback

[@oahuhawaii2141]

At 04:00, you wrote log x¹⁰ = 0 , which doesn't make sense to do -- why raised x to the 10th power, only to discard that in the next step? If you meant log₁₀(x) then use subscripts in the proper location.