C2 Logs Help

Hi!

I was doing a C2 past paper and came across this question - it seems to involve working backwards from a log graph. The only problem is I don't really understand how to do it...

I got as far as finding the gradient as 3. I'm not entirely sure what to do after that so if someone could help me through it i'd appreciate it.

so y = 3x + 2

log(y) = log(x^3) + 2

y = 10^3 x^3

y = 1000x^3

Thanks.. but two questions if I may:

1) Where does the +2 go?

2) How do I know if a graph is of the form log(y) = klog(x) + c
or just
log(y) = kx + c

Assuming I'm not given the axis in the first place? I've always been slightly confused about that.

That's not correct. We have $\log_{10} y = \log_{10} x^3 + 2 = \log_{10} x^3 + \log_{10} 10^2 = \log_{10} 100x^3$

So "cancelling" the logs, we have: $y = 100x^3$.



As above. It shouldn't have gone.



You will be told by either axis labels or "this is a graph of $\log y$ v/s $x$" in which case your graph is $\log y = k x + c$ or "this is a graph of $\log y$ v/s $\log x$" in which case your graph is $\log y = k \log x + c$ . You getting it?




By the way, quote me by clicking the reply button at the bottom right of my post so I get a notification.

Ah right that makes a lot more sense. Thank you! I guess I just need to learn the relationship between y=mx+c and the log graphs... you'd think doing physics would make that simple.