Hi,
I am really stuck on how you deal with with an exponential equation something like this:
x^y - 5 * x^y = 0 I know I cant multiply 5 * x^y as they have a different base (right?)
How do i simplify this and get the variables/exponents together?
Thanks
That is not the correct equation.
The actual equation i am working on is:
16^x - 5 * 8^x = 0
I have tried converting into base of 2 so:
(2^4)^x - 5 * (2^3)^x = 0
= 2^4x - 5 * 2^3x = 0
but I have no idea how to deal with the -5 * part of the equation.
Thanks
Yes.
$x\ is\ a\ real\ number \implies 2^x > 0 \implies \left(2^x\right)^3 > 0 \implies 2^{3x} > 0 \implies 2^{3x} \ne 0.$
I think the easiest way to deal with this is:
$16^x - 5 * 8^x = 0 \implies 16^x = 5 * 8^x \implies$
$\left(2^4\right)^x = 5 * \left(2^3\right)^x \implies$
$2^x = 5 \implies$
$ln(2^x) = ln(5) \implies$
$x = \dfrac{ln(5)}{ln(2)}.$
Edit: The answer in terms of log base 2 is more succinct, but it does not readily lead to a numeric approximation whereas an answer in terms of log base e can easily be computed on a scientific calculator.