This form of equation cause me a lot of problems. I know it involves several steps, but i am getting stuck right at the start.
2^x + 2^-x =5
My teacher said to start it off by setting it equal to zero, but after that I don't know what to do.
This form of equation cause me a lot of problems. I know it involves several steps, but i am getting stuck right at the start.
2^x + 2^-x =5
My teacher said to start it off by setting it equal to zero, but after that I don't know what to do.
multiply each term by $\displaystyle 2^x$ ...
$\displaystyle 2^{2x} + 1 = 5 \cdot 2^x$
let $\displaystyle u = 2^x$ ...
$\displaystyle u^2 + 1 = 5u
$
$\displaystyle u^2 - 5u + 1 = 0$
$\displaystyle u = \frac{5 \pm \sqrt{21}}{2}$
$\displaystyle 2^x = \frac{5 + \sqrt{21}}{2}$
$\displaystyle 2^x = \frac{5 - \sqrt{21}}{2}$
finally, use logarithms to solve for $\displaystyle x$