Question

Log1/6(5). I am absolutely clueless as to what i'm supposed to do. The 1/6 is below the log.

Answer 1

Question: Evaluate/death stare at $log_{\frac{1}6}(5)$.

Let's talk about what logarithms mean.

Suppose $log_{\frac{1}6}(5)=x$.

That's the same thing as $5=(\frac{1}6)^x$. It's just been simplified.
(Logarithms are the inverse operations of exponents)

We can use a calculator to evaluate logarithms that are in base 10.
(In this case, the base is 1/6)

How can we change this so that it uses just base 10?
We can use something called the change-of-base formula.

Here's what the change of base formula looks like.

$log_x(n)=\frac{log_y(n)}{log_y(x)}$

In this case, we'll set the base $y$ to be 10. (you can set it to whatever you want) $x$ is going to be 1/6, and $n$ is 5.
When the base is 10, we don't have to write it, it's like a plus zero or a times one.

$log_\frac{1}6(5)=\frac{log(5)}{log(\frac{1}6)}$

Punch this into a calculator to find your answer.

$\frac{log(5)}{log(\frac{1}6)} \approx \boxed{-0.8982444017}$

You can always check your answer if you need to, of course.

$(\frac{1}6)^{-0.8982444017} \approx 5$