# Thread: Solve for x using Log

1. ## Solve for x using Log

(2^-x)sinx = 1/2x - 1
My teacher said to use logs, but I'm useless at them
I would really appreaciate any help given

2. Originally Posted by Zel
(2^-x)sinx = 1/2x - 1
My teacher said to use logs, but I'm useless at them
I would really appreaciate any help given
Having two different transcendental functions makes that a really difficult equation, particularly with that (1/2)x- 1. Unless you mean $\displaystyle (1/2)^x$= 2^{-x}[/tex]. If so, it is still difficult but you might be able to write sin(x) as $\displaystyle \frac{e^{ix}- e^{-ix}}{2i}$ and write 2^{-x} as $\displaystyle e^{-xln(2)}$

3. Originally Posted by Zel
(2^-x)sinx = 1/2x - 1
My teacher said to use logs, but I'm useless at them
I would really appreaciate any help given
Can you add some brackets to make it clear if the right hand side is:

$\displaystyle \frac{1}{2x-1}$

$\displaystyle \frac{1}{2}x -1$

$\displaystyle \frac{1}{2x}-1$

or whatever?

I also doubt that this can be rearranged as required.

CB

4. Originally Posted by HallsofIvy
Having two different transcendental functions makes that a really difficult equation, particularly with that (1/2)x- 1. Unless you mean $\displaystyle (1/2)^x$= 2^{-x}[/tex]. If so, it is still difficult but you might be able to write sin(x) as $\displaystyle \frac{e^{ix}- e^{-ix}}{2i}$ and write 2^{-x} as $\displaystyle e^{-xln(2)}$
The mixture of exponential and linear functions of x still means this is likely to involve our old favourite, Lambert's W.

CB