Question

Are y=log(x+1) and y=10^x-1 symmetric about the line y = x ?

Answer 1

They are symmetrical about the y=x because g(x)=10^x-1 is the inverse of f(x)=y=log(x+1).

To confirm, if f(g(x))=x then g is the inverse of f, and g and f are symmetrical about y=x.