Thread: need help with solving equations

1. need help with solving equations

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.

2. Originally Posted by mtt0216
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 $\displaystyle x$

3. thanks a lot .. How would this problem change if e was substituted for 2.

4. Originally Posted by mtt0216
thanks a lot .. How would this problem change if e was substituted for 2.
no change ... in fact, would make the final step easier when solving using the natural log.