SOLUTION: solve 2^-x=.647 and logb(lower case b)3=2

Algebra ->  Test  -> Lessons -> SOLUTION: solve 2^-x=.647 and logb(lower case b)3=2      Log On


   

Question 536988: solve 2^-x=.647 and logb(lower case b)3=2
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
In this website, I type "{" 3 times, then "log (b,3)=2" and then "}" 3 times to get log+%28b%2C3%29=2.
I type "{" 3 times, then "log (3)" and then "}" 3 times to get log+%283%29, which means logarithm of 3 in base 10 (10 omitted).
I assume that's what you meant. You wanted that b as a subscript, right?
log+%28b%2C3%29=2 means that b%5E2=3 and you know what number you have to square to get 3: b=sqrt%283%29
I do not see an elegant solution to the other problem. All I can think to do is this:
2%5E%28-x%29=.647-->log%28%282%5E%28-x%29%29%29=log%28.647%29-->%28-x%29log%282%29=log%28.647%29-->xlog%282%29=-log%28.647%29-->x=-log%28.647%29%2Flog%282%29
and that would give you an approximate value of 0.628.