Can you Solve Harvard University Admission Test? ✍️🖋️📘💙

[@Winter_spirit_Claudia]

Thats so cool!

[@walterwen2975]

Harvard University Admission Test: 100^√x = √(1000ˣ); x =?
100^√x = (10²)^(√x) = 10^(2√x), √(1000ˣ) = √(10³ˣ) = 10^(3x/2); 10^(2√x) = 10^(3x/2)
2√x = 3x/2, 3x = 4√x, 3x - 4√x = (√x)(3√x - 4) = 0, √x = 0 or 3√x - 4 = 0
x = 0 or 3√x = 4, √x = 4/3, x = (4/3)² = 16/9
Answer check:
x = 0: 100^√x = 100⁰ = 1, √(1000ˣ) = √(1000⁰) = 1; Confirmed
x = 16/9: 100⁴⸍³ = 10⁸⸍³, √(1000¹⁶⸍⁹) = (10³)⁸⸍⁹ = 10⁸⸍³; Confirmed
Final answer:
x = 0 or x = 16/9

[@DhannyTK]

Taking log on both sides would also be similar and easier

[@ManojkantSamal]

X=16/9 may be
Explain later

[@MohitSingh-mf2nn]

Is it really that hard it is too easy

[@geogeo6071]

I love hearing your baby

[@superacademy247]

Thanks so much! Happy new year 🎉🎁🥳🎄

[@InnaMarthin]

X=0

[@prollysine]

()^2 , 100^(2Vx)=1000^x , 2Vxlog100=xlog1000 , 2*log(Vx)*2=3*x , 4*Vx=3*x , / : Vx , 4/3=Vx , / ()^2 , x=16/9 ,
test , 100^V(16/9)=~464.159 , V(1000^(16/9)))=~464.159 , same , OK ,