# Thread: Logarithmic system of equations

1. ## Logarithmic system of equations

I have the value of x (used my graphing calculator), but I need to be able to show the work. Can anyone give me an idea of what to do here?

$
\log_4 x = 2^{(x-6)}
$

2. Originally Posted by p3rsonman
I have the value of x (used my graphing calculator), but I need to be able to show the work. Can anyone give me an idea of what to do here?

$
\log_4 x = 2^{(x-6)}
$

1. This obviously has two real roots if it has any

2. Numericaly they are 1.04573 and 6.42411

3. This may have a closed form solution in terms of the Lambert W function but I will have to look into that.

4. The inverse symbolic calculator does not recognise either of these (when extended to 11 significant digits).

RonL