If 4^x +4^(-x) = 7, hence 8^x +8^(-x) = .......

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If 4^x +4^(-x) = 7, hence 8^x +8^(-x) = .......

Mathematics
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log x to the base 4 + log - x to the base 4 = 7 Im unsure if thats right
the choices are : a) 15 b) 18 c) 21 d) 24 e) 30
Its 18 ( option b) Through trial and error you find x to be something around 1.4 Substitute that value in the second formula you get 18.4 So the answer is 18

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that's right the answer is 18. but how do you get x around 1.4? i dont understand.
first try x = 2 in the first formula its too high so then i tried x as 1.5 It was closer !.3 was too low 1.4 was pretty close I finally got it as somewhere around 1.39
thankyou :)
medal??
just kidding
haha you dont want it? should i undo that?
Begini Dinda, \((a^3+\frac{1}{a^3})^2=a^6+2+\frac{1}{a^6}\) \((a^2+\frac{1}{a^2})^3=a^6+3a^2+\frac{3}{a^2}+\frac{1}{a^6}\) Akibatnya \((a^3+a^{-3})^2=(a^2+a^{-2})^3+2-3(a^2+a^{-2})\)..............(*) Sekarang ambil \(a=2^{-x}\) Maka kita peroleh \(a^2+a^{-2}=7\) dan kita inging mencari \(a^3+a^{-3}\) Dari (*) kita peroleh \(a^3+a^{-3}=7^3+2-3(7)=324\) Dengan demikian \(a^3+a^{-3}=\sqrt{324}=18.\)

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