Alan

Or it could be 3^(2^x) = 195 in which case

Take logs:

(2^x)ln(3) = ln(195) or 2^x = ln(195)/ln(3)

Take logs again:

xln(2) = ln( ln(195)/ln(3) )

x = ln( ln(195)/ln(3) )/ln(2)

$${\mathtt{x}} = {\frac{{ln}{\left({\frac{{ln}{\left({\mathtt{195}}\right)}}{{ln}{\left({\mathtt{3}}\right)}}}\right)}}{{ln}{\left({\mathtt{2}}\right)}}} \Rightarrow {\mathtt{x}} = {\mathtt{2.262\: \!941\: \!541\: \!431\: \!602\: \!2}}$$

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For info:

€ =Euro

£ = pound

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-2^2 = -4

(-2)^2 = +4

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Infinity divided by any finite number is still infinity!

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You would generally apply the rule to the final result.

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Part 2:  Gary has no more than $2.75  (because he can buy at most 5.5pounds of potatoes)

Part 3: 2.5 pounds of onions cost 2.5*$1.25 = $3.125, which is more than Florence wants to spend.

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$$2^{-2}=\frac{1}{2^2}=\frac{1}{4}$$

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Do the whole number part first:  4 + 3 = 7

Now do the fractions: 4/10 + 9/10 = 13/10  This is 1 3/10.

Add this to 7 to get 8 3/10

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I assume you want to find the length of the diagonal of the rectangular roof.  This is done using Pythagoras's theorem with a = 40, b = 20.  So c, the length of the diagonal is:

$${\mathtt{c}} = {\sqrt{{{\mathtt{40}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{20}}}^{{\mathtt{2}}}}} \Rightarrow {\mathtt{c}} = {\mathtt{44.721\: \!359\: \!549\: \!995\: \!793\: \!9}}$$

or c ≈ 44.7 feet

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0.000078 is 78x10^-6 in engineering notation.

Engineering notation is a little like scientific notation except that the power to which 10 is raised is must be a multiple of 3.

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