# 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#