Monday, April 29, 2013

solve: (5/9)^x=8^(1-x)

log functions are inverses of exponential functions. We have two choices. In this case we'll use log base 8 (can you see why?). 
%285%2F9%29%5Ex=8%5E%281-x%29
log_base+8%28%285%2F9%29%5Ex%29=log_base+8%28%288%29%5E%281-x%29%29%29
First we rewrite so that out exponents are now products and we use the fact that

log_base+8%28%288%29%29=1
to simplify our equation and we get:
x%2Alog_base+8%285%2F9%29=1-x
x%2Alog_base+8%285%2F9%29%2Bx=1
x%2A%28log_base+8%285%2F9%29%2B1%29=1

x=1%2F%28log_base+8%285%2F9%29%2B1%29
Posted by at
Labels: , ,

No comments:

Post a Comment

Subscribe to: Post Comments (Atom)