SOLUTION: Find the exact solution 8^(x-1)=16^(x+3)
I keep getting 3 log(2^x-1)=4 log(2^x+3)
which I turn into a big string of :
3 log (2) + x log (2) - log (2) = 4 log (2) + x log (2) +
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Question 799369: Find the exact solution 8^(x-1)=16^(x+3)
I keep getting 3 log(2^x-1)=4 log(2^x+3)
which I turn into a big string of :
3 log (2) + x log (2) - log (2) = 4 log (2) + x log (2) + 3 log (2)
Which I simplify to :
x log (2)= 5 log (2) + x log (2)
but that doesnt seem right, wont the x log (2)'s cancel out?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the exact solution 8^(x-1)=16^(x+3)
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Change both sides to base "2":::
(2^3)^(x-1) = (2^4)^(x+3)
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= 2^(3x-3) = 2^(4x+12)
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= 3x-3 = 4x+12
x = -15
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Cheers,
Stan H.
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Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
You started off on the right foot, but you will have a much easier time of it if you take the base 2 log of both sides.
}\ =\ 2^{4(x\,+\,3)})
}\right)\ =\ \log_2\left(2^{4(x\,+\,3)}\right))
\right)\log_2(2)\ =\ \left(4(x\,+\,3)\right)\log_2(2))
But since \ =\ 1)
\ =\ 4(x\,+\,3))
from which it follows:
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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