A few questions about this function: F(x) = log(base 7)x?

Question

Is the function's x-intercept (1,0)? Is the y-intercept (0,3)? Is the function increasing or decreasing? Is its range y > 0? Is its domain x > 7?

Answer 1

Log[7](x) = ln(x) / ln(7) by change of base formula
So analyze ln(x) / ln(7).

ln(x) is always increasing and ln(7) is just a constant so we can conclude that ln(x) / ln(7) is increasing.

ln(1) = 0 so yes ln(1) /ln(7) = 0/ln(7) = 0 so (1,0) is right

What about the y intercept? well what happens when x is 0?
ln(0) is undefined so there is no y-intercept.

Domain: well what is the domain of ln(x)? It's x>0.
Since Log[7](x) = ln(x) / ln(7) we haven't changed our domain at all it's still It's x>0.

Range: the range of ln(x) / ln(7) is the same as range of ln(x) all real numbers

Answer 2

F(x) = log[7](x) = ln(x)/ln(7)

yes x intercept is (1,0)
there is no y intercept
its monotonically increasing everywhere
domain is x>0

Answer 3

1) yes
2) no there is no y intercept because x can´t be zero
3) No. Its range is -infnity to +infinity
4)No .its domain is x>0