I need to find the logarithmic curve between two points $$A(0,5),\quad B(180,9)$$
We know that the formula for logarithmic function is: $\;f(x) = \log(x)\,\;$so $$ 5 = \log(0),\quad 9 = \log(180)$$
But that's impossible because $\log(0)$ is undefined. What Did I do wrong?
Following the below advice I'm still stuck
$a^5=0-b$ and $a^9=180-b$
$$a^9 = 180+a^5 $$ $$a^4 = 180$$ $$a = 3.66$$
Now let's plug a in our original formula
$$3.66^5 = -b$$ $$b = -656.7$$
$$f(x) = \log3.66(x+656.7)$$
I did a little bit of fiddling with a graph and at the end of the day what I was looking for was
$$f(x) = \log1.77(x-5)$$
I would be awesome to understand how to achieve this result without playing randomly with excel.