Harvard Entrance Exams || No Calculator Allowed

[@aku7598]

4^x=8 2^3=8 So we root 4 and then cube it. 4^x= 4^(3/2)

[@RyanLewis-Johnson-wq6xs]

4^x+4^x=16 x=1.5=3/2=1 1/2

[@adgf1x]

=>2^2x=2^3=>x=3/2=1.5ans

[@adgf1x]

log 8 base 4=x=>x=log 4 base4+log 2 base4=1+1/log 4base2+1+1/2=3/2=1.5ans

[@bernardstoffels1673]

4^x+4^x=16 2.4^x =16 4^x=8 2^2x=2^3 2x=3 x=3/2

[@MrMousley]

4^x + 4^x = 16 So 4^x = 8 Now get both sides down to 'a power of 2' (2^2)^x = 2^3 2^2x = 2^3 2x = 3 x = 3/2

[@pbworld7858]

Yes, that's how I did it in my head within a few seconds. When it said Harvard, I thought it was going to be difficult.

[@RobotKiwiTheFailureKid]

X=1.5

[@RealQinnMalloryu4]

{4x+4x ➖ }+{4x+4x ➖ }={8x^2+8x^2}=16x^4: 2^4x^4 2^2^2x^2^2 1^1^1x^1^2 x^1^2 (x ➖ 2x+1)