## anonymous 5 years ago If 4^x +4^(-x) = 7, hence 8^x +8^(-x) = .......

1. anonymous

log x to the base 4 + log - x to the base 4 = 7 Im unsure if thats right

2. anonymous

the choices are : a) 15 b) 18 c) 21 d) 24 e) 30

3. anonymous

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

4. anonymous

that's right the answer is 18. but how do you get x around 1.4? i dont understand.

5. anonymous

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

6. anonymous

thankyou :)

7. anonymous

medal??

8. anonymous

just kidding

9. anonymous

haha you dont want it? should i undo that?

10. watchmath

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 $$a^3+a^{-3}=\sqrt{324}=18.$$

Find more explanations on OpenStudy