Question

The x-intercept of the graph of f(x)=3log(x-5)+2 is:

A. 10^(2/3)+5
B. 10^(-2/3)+5
C. 10^(-2/3)-5
D. 10^(2/3)-5

Answer 1

I have a graphing calculator available if I need one

Answer 2

B

Answer 3

Thank you. Any explanation would also be awesome!

Answer 4

Sure. I'm going to try to explain this in the easiest manner possible. Since you want to find the x-intercept, your y-intercept has to equal 0. In which case your equation would be
0=3log(x-5)+2 <--- sub in 0 for your y-value (f (x))
-2 = 3log(x-5) <----- bring 2 over to the other side
-2/3 = log(x-5) <---- divide by 3 ( NOTE : you CAN NOT divide by (x-5) )
10^ (-2/3) = x-5 <---- use the power log
10^ (-2/3) + 5 = x <---- bring the 5 over to the other side

Hope this makes sense. I tried :P

Answer 5

Yeah, that makes total sense! Thank you!

Answer 6

Anytime! :)