Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

thankyou :)

Answer 7

medal??

Answer 8

just kidding

Answer 9

haha you dont want it? should i undo that?

Answer 10

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