How do you solve #3^b=17#?
2 Answers
Mar 15, 2018
Explanation:
Lets take the logarithm of both sides of the equation:
then divide both sides by
My pocket calculator (HP 15C) reads
Mar 15, 2018
Real solution:
#b = ln 17 / ln 3#
Complex solutions:
#b = (ln 17 + 2kpi i)/ ln 3" "# for any integer#k#
Explanation:
Given:
#3^b = 17#
Note that
So, if
So while we find the real solution by taking the real valued natural log, we can also add any integer multiple of
Take natural log of both sides of the given equation to get:
#b ln 3 = ln 17 color(grey)(+ 2kpi i)#
Divide both sides by
#b = (ln 17 color(grey)(+2kpi i))/ln 3#