SOLUTION: solve for X: 3^(x-1)+3^(x-2)=81-3^(x+3)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve for X: 3^(x-1)+3^(x-2)=81-3^(x+3)      Log On


   

Question 764164: solve for X:
3^(x-1)+3^(x-2)=81-3^(x+3)
Answer by lwsshak3(11628) About Me  (Show Source):
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solve for X:
3^(x-1)+3^(x-2)=81-3^(x+3)
***
3^(x-1)+3^(x-2)+3^(x+3)=81
3%5E%28x-1%29%281%2B3%5E-1%2B3%5E4%29=81
3^(x-1)(82+1/3)=81
3^(x-1)(247/3)=81
3^(x-1)=81*3/247≈0.9838
take log of both sides
(x-1)log3=log(0.9838)
x=(log(0.9938)/log3)+1
x≈0.9851
Check:
3^(x-1)=3^(.9851-1)≈0.9838
3^(x-2)=3^(.9851-2)≈0.3279
3^(x+3)=3^(.9851+3)≈79.6858
0.9838+0.3279+79.6858≈80.9965≈81