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Core math

The variables x and y satisfy the equation x^n y = C, where n and C are constants . When x = 1.10, y= 5.20 and when x= 3.20, y= 1.05.(i) Find the values of n and C(ii) Explain why the graph of ln y against ln x is a straight line.

Reply 1

MindMax2000

Universities Forum Helper

Original post by Crazy_tae

I presume you mean (x^n)y = C
When x = 1.1, y = 5.2: (1.1^n)5.2 = C
When x= 3.2, y = 1.05: (3.2^n)1.05 = C

You have simultaneous equations. I like the substitution method, so I would let one equation equal the other, since they both conveniently both have C in them. When you manage to get the term with n on one side of the equation, take the log of the equation to find n. C will be a doddle after that.

(x^n)y = C
nln(x) + lny = lnC (which I will let = C because it doesn't change the fact it's still a constant)
lny = -nln(x) + C Try drawing the graph on log paper. It should resemble a straight line.