Finding point of intersection of two lines on semi log chart

somathinred

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I haven't taken math since high school so I've forgotten much math, and solving this question is required for my job. Hopefully, someone can explain how to solve this problem, as I haven't been able to find an explanation online that I could easily follow.

-I need to find the point of intersection of two lines that are to be drawn on a semi log scale (y axis is log, x axis is not log).
-Line 1 is drawn from points (0, 35.20) and (0.5, 44.205)
-Line 2 is drawn from points (1, 35.20) and (1.5, 40.165)

What is the point of intersection of these two lines on a semi log chart? What is the formula? Thanks.
 
solving this question is required for my job


I need to find the point of intersection of two lines that are to be drawn on a semi log scale (y axis is log, x axis is not log).
-Line 1 is drawn from points (0, 35.20) and (0.5, 44.205)
-Line 2 is drawn from points (1, 35.20) and (1.5, 40.165)


What is the point of intersection of these two lines on a semi log chart? What is the formula?

Hi somathinred:

Assuming common LOGs (base10)

Given two points (X1, Y1) and (X2, Y2), the linear equation is

\(\displaystyle

y = \dfrac{LOG(Y1)-LOG(Y2)}{X1-X2} \cdot (x - X1) + Y1

\)


Substitute the known coordinates for points (X1, Y1) and (X2, Y2) on Line1 and simplify.


:idea: You may pick either point to be (X1, Y1); the other will be (X2, Y2)


y = 0.1978574640x + 35.2



Make the same substitutions for points (X1, Y1) and (X2, Y2) on Line2 and simplify.


y = 0.1146102160x + 35.08538978



Set these two expressions for y equal to each other.


0.1978574640x + 35.2 = 0.1146102160x + 35.08538978


Now solve this equation for x, by using a solver like this one.


Substitute the solution into either equation for Line1 or Line2, to calculate the corresponding y.


These steps give the intersection point (-1.3767, 34.9276)


log-lin1.jpg




You may read more about these LOG-LIN graphs at Wikipedia.


The linear equations graphed above (with vertical LOG scale and horizontal LINEAR scale) correspond to the following exponential functions.


f(x) = [0.1584893192*10^36] 10^(0.1978574640x)

g(x) = [0.1217278020*10^36] 10^(0.1146102160x)


log-lin2.jpg


Cheers :)
 
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