Answer:
0.540
Step-by-step explanation:
Hi there,
To get started in order to solve this, please recall the property of logarithms.
This question is a bit tricky, but doable. Best way to solve this is first compare the two functions:
Now, let's see what the function gives at 13 and 1:
Something to recognize is that 1 to the power of <em>anything</em> is just 1, so f(1) is reduced to:
We are making progress!
Next, we can set both f(13) forms equivalent to each other, watch this:
but we know what f(1) is equal to, and let's substitute our knowns:
the c constant on both left and right side cancel out:
Now, take the logarithm form of both side of the equation. I used natural log, but you can also use common logs:
⇒
this was performed using <em>the power log rule. </em>
Isolate k:
using a calculator.
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thanks,