Are exponential and logarithmic functions symmetric with respect to the line y = x, regardless of whether a is greater than 1 or less than 1?

Are exponential and logarithmic functions symmetric with respect to the line y = x, regardless of whether a is greater than 1 or less than 1?

Yes. Whether a is greater than 1 or less than 1

Let f (x) = coswx (W > 0), after the image of y = f (x) is shifted to the right π / 3 unit length, the resulting image is coincident with the original image, then the minimum value of W is? My practice is that because of the coincidence, the translation period is an integral multiple of 2 π / W, so w π / 3 = 2 π / W, w = root 6

When the image of the function f (x) = coswx (W > 0), y = f (x) is shifted to the right by π 3 unit length, the resulting image coincides with the original image
Let cosw (x - π / 3) = coswx
That is cos [wx-w π / 3] = coswx
So w π / 3 = 2K π, K ∈ Z
The solution is w = 6K, K ∈ Z
Because w > 0
So the minimum value of W is 6