logarithmic function between two points I need to find the logarithmic curve between two points

Emmy Dillon

Emmy Dillon

Answered question

2022-06-24

logarithmic function between two points
I need to find the logarithmic curve between two points
A ( 0 , 5 ) , B ( 180 , 9 )
We know that the formula for logarithmic function is: f ( x ) = log ( x ) so
5 = log ( 0 ) , 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
then
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 ) = log 3.66 ( 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 ) = log 1.77 ( x 5 )
I would be awesome to understand how to achieve this result without playing randomly with excel.

Answer & Explanation

Hadley Cunningham

Hadley Cunningham

Beginner2022-06-25Added 20 answers

Assume that f ( x ) = l o g ( a x + 10 ) + c
We have f ( 0 ) = 5, so
f ( 0 ) = l o g ( 0 x + 10 ) + c = 5
So c is 4. Now we know that:
f ( x ) = l o g ( a x + 10 ) + 4
We have f ( 180 ) = 9, so
f ( 180 ) = l o g ( 180 a + 10 ) + 4 = 9
that is,
l o g ( 180 a + 10 ) = 5
a = ( 10 5 10 ) / 180
hence f(x) is (you can do the required simplification if you want to...):
f ( x ) = l o g ( ( 10 5 10 ) / 180 ) x + 10 ) + 4
Needless to say that there may be other functions that could be logarithmic and can pass by A, B.
Erin Lozano

Erin Lozano

Beginner2022-06-26Added 7 answers

Try to use f ( x ) = log ( a ( x b ) ).Then try find the values of a and b.

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