I'm given the following equations of which I need to find the solutions for algebraically.
$ab = 8$
$c^b = 256$
My first thought was to use logarithms, but I got a bit lost in doing so
$\log_2 2^a = \log_2 c$
$a = \log_2 c$
$\log_c c^b = \log_c 256$
$b = \log_c 256$
And plugging those into the first equation I get
$(\log_2 c)(\log_c 256) = 8$
However from here, I'm at a loss on what to do. Can someone help me out here? Thanks!