Exponential functions and inverses
Author: Doug Kuhlmann

Move the slider to change the base.
Move point A along X-axis to change B & B'.

Change the base of the function b^x

Lines & points

Show inverse

For what value of a is  \[b^x \] tangent to \[
\log _b x
\]?

Show question

\[
e^{\frac{1}
{e}} 
\]

Show answer

Point on the inverse with this y-coordinate

Point on a^x with this x-coordinate

b = 1.605 (slider from 1 to 2, step 0.0050)
f(x) = b^(x)
A = Point(xAxis)
B: (x(A), f(x(A)))
B': (f(x(A)), x(A))
loc1 = Locus(B', A)
b_1 = Segment(B, B')
A': (0, x(A))
d = true
e = true
SQ = true
SA = true
g = Segment(A', B')
i = Segment(B, A)