C2 Logs

This from the MEI C2 paper from june 2012.

I basically wrote the 4 logs in exponential form and I got x = 10, 10^5 and y = 10^5, 10^17.
Then I found the equation, y = 10^12x -(10x10^11).

Is this miserably wrong?

Not quite sure what you've done but it's not right...

Don't worry about the logs on the axes for the moment: first treat this as any normal straight line and from the two points, work out the gradient, m. Then using y=mx+c, work out the intercept by substituting in one of the points because you have a straight line here. Work out the gradient and intercept and tell me what you get, then we can move on to the next bit.

Haha, I got y = 3x + 2.

Excellent - that is right. Now replace the "y" by the quantity on the y-axis, and "x" by the quantity on the x-axis.

log y = 3logx + 2?

y = 100x?

$\log_{10}y - \log_{10}x^3 = 2$

$\log_{10}(\frac{y}{x^3})$ = 2

$10^2 = \frac{y}{x^3}$

$y=100x^3$

??

Yeah - that's it.

wagwan cheers