I want to plot the segment [AB] on a log-log graph. I have the point A, the slope and B.y. How to find B.x?
2026-03-29 04:34:30.1774758870
Log-Log graphic : calculate point B.x, with point A, the slope and B.y
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Given a function y= f(x), on log-log paper by marking a point x on the horizontal axis and and y on the vertica axis we are actually marking log(x) and log(y) so that a linear graph, instead of giving "y= mx+ b", gives log(y)= m log(x)+ b and,taking the exponential of both sides y= Bx^m where B= e^b.
If you have a point, (Ax,Ay) and slope m the we have log(Ay)= m log(Ax)+ b so b= log(Ay)- log(Ax)= log(Ay/Ax) so that e^b= Ay/Ax.
So y= (Ay/Ax)x^m. If y= By then we have By= (Ay/Ax)x^m so that x^m= AxBy/Ay so that $Bx= x= \sqrt[m]{AxBy/Ay}$.