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Question Number 145769 by Engr_Jidda last updated on 07/Jul/21

find x if  2^x +2^(3x) =16

findxif2x+23x=16

Commented by 7770 last updated on 08/Jul/21

2^x +2^(3x) =16   let 2^x =m  m+m^3 =16   m^3 +m−16=0  let f(x)=m^3 +m−16   f^′ (x)=3m^2 +1  let the initial guess m be 0  using nri     m_1 =m_0 −((f(x))/(f^′ (x)))   m=2.387686553...    2^x =m   2^x =2.387686553...   x=((ln2.387686553...)/(ln2))   x≈1.255613

2x+23x=16let2x=mm+m3=16m3+m16=0letf(x)=m3+m16f(x)=3m2+1lettheinitialguessmbe0usingnrim1=m0f(x)f(x)m=2.387686553...2x=m2x=2.387686553...x=ln2.387686553...ln2x1.255613

Answered by mr W last updated on 07/Jul/21

let t=2^x   t^3 +t−16=0  Δ=(1/(27))+64>0  (√Δ)=((√(5187))/9)  ⇒t=((((√(5187))/9)+8))^(1/3) −((((√(5187))/9)−8))^(1/3)   ⇒x=log_2  (((((√(5187))/9)+8))^(1/3) −((((√(5187))/9)−8))^(1/3) )          ≈1.255613

lett=2xt3+t16=0Δ=127+64>0Δ=51879t=51879+835187983x=log2(51879+835187983)1.255613

Commented by Engr_Jidda last updated on 08/Jul/21

thank you sir

thankyousir

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