# How do you evaluate #log_169 (-13)#?

##### 3 Answers

A log expression in this form is asking the question...

"what power of 169 will give -13?"

OR" What index of 169 will make -13?"

I

#### Explanation:

For any Real value of

So to find a value for

Note that

In general, if

Use the change of base formula to find:

#log_169 (-13)#

#=ln(-13)/ln(169)#

#=ln(-13)/ln(13^2)#

#=(ln(13)+pi i)/(2 ln(13))#

#=1/2 + pi/(2ln(13))i#

This is the principal value of the Complex logarithm.

Other values that satisfy

#### Explanation:

I think that I could make a compromising answer.

Use that, for

Now,

using

If students are not to be burdened, these questions could be

reserved for Extraordinary Talent Examinations, after doing good

home work on the answer....