SOLUTION: Which statements represent the relationship between {{{ y=3^x }}}} and {{{ y=log_3 (x) }}}? Choose all the correct answers: a) The graphs of the functions are symmetric about t

Question 1105190: Which statements represent the relationship between } and ?
Choose all the correct answers:
a) The graphs of the functions are symmetric about the line y=x.
b) The equation is the logarithmic form of .
c) The functions are inverses of each other.
d) The graphs of the functions are symmetric about the line y=0.
I think the answers are () and (d). But I'm not so sure. This is very urgent, so immediate help will be VERY appreciated!!! Thanks!! :)
Found 2 solutions by Boreal, KMST:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
y=3^x
x=3^y
log(3)x=log(3) (3^y)=y, so log3 (x)=y for inverse.
So long as it is written as log to the base 3 of x then the two are inverses but symmetric around the line y=x
So C.
y=3^x has an asymptote at y=0 but is not symmetric around it.
y=log3 (x) has an asymptote of x=0 but is not symmetric around it.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I would agree if your teacher said that is the logarithmic form of ,
because when one equation is true so is the other,
but option b does not say that.
Neither graph by itself shows any symmetry, but they are inverse functions, and as you interchange x for y to get an inverse function, you are flipping the graph so that the x-axis becomes the y-axis and vice versa. That make inverse mirror images of each other, and the line y=x is the mirror.
This is the graph of ,
and the graph of looks like this:
.
Both graphs together, along with the line look like this:
.
You know that the line is the x-axis.
What do you think of choices a and d now?
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