SOLUTION: Determine (8x)^x if , 9^x+2=240+9^x
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Question 1101105: Determine (8x)^x if , 9^x+2=240+9^x
Answer by Benbuks(2) (Show Source): You can put this solution on YOUR website!
I would presume you meant to type
9^(x+2)=240 + 9^x .
If so, the solution goes thus
the given equation can be rewritten as
9^x•9² =240 + 9^x
→ 81•9^x = 240 + 9^x
Now, lets do a quick transformation,
let p= 9^x
Thus, we have
81p= 240 + p
Collect like terms
→ 81p -p= 240
→80p=240
→ p=240/80 =3
∴p=3
recall that
p= 9^x ,
→ 3= 9^x
→3¹ =( 3²)x
→ 3¹ = 3^(2x)
3 Cancels out
→ 1= 2x
Or
→ 2x=1
∴ x= 1/2
Now ,
(8x)^x. would be
[8× 1/2) ^(1/2) = 4^(1/2)
= √(4) = 2
∴ANSWER : 2
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