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Logarithmic data transformations

Question 1 of 8

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The table gives explanatory values \(x\) and response values \(y\)

\(x\)	\(10\)	\(10000\)	\(100000\)	\(1000000\)	\(10000000\)	\(1000000000\)
\(y\)	\(5\)	\(80\)	\(125\)	\(180\)	\(245\)	\(405\)

(a)3 marks

Find the missing entries in the transformed x-row

\(x\)	\(10\)	\(10000\)	\(100000\)	\(1000000\)	\(10000000\)	\(1000000000\)
\(y\)	\(5\)	\(80\)	\(125\)	\(180\)	\(245\)	\(405\)
\(\log_{10}(x)\)	?	4	5	6	?	?

\(\log_{10}(x)\) when x = 10 \(\log_{10}(x)\) when x = 10000000 \(\log_{10}(x)\) when x = 1000000000

(b)1 mark

Are all successive slopes in the transformed coordinates equal?

Yes. All successive transformed slopes are equal

No. The successive transformed slopes are not all equal