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The latest generation car shifts the goalposts to another dimension.

► CAR’s BMW i8 long-term test review► Hybrid i8 costs £105k; 0-62 in 4.4sec► Our conclusion after seven months BMW’s designers must regularly frequent a five-star hotel that has its sole sun lounger in a fenced-off recess under a small, sharp-edged flight of stairs.

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Because 1 is the same thing as 10, we will get 10; and as it operates on everything in between, we will get everything in between, as well.0577So, there is massive variance in our inputs and massive different possible inputs that we can put in.0585There is a very, very small range of outputs that we will end up getting out of it.0589This behavior makes logarithms a great way to measure quantities that can be vastly different--0594things that can have really huge variance in what you are measuring.0599But we want an easy way to compare or talk about them; we have to be able to talk about these things.0602They come up regularly, and we don't want to have to say numbers like 10 billion or 9 billion 572 million.0607We want some number that is fairly compact--that doesn't require all of this talking.0614So, we use logarithms to turn it into this much smaller, more manageable number that makes sense, and we can understand, relative to these other things.0618Earthquake magnitude is one of the things that is measured on it.0625It is measured on the Richter scale, which is a logarithmic scale.0629Sound intensity is another one; it is measured in decibels, which is another logarithmic scale.0632Acid or base concentration is measured on the p H scale; we will actually have examples about that in Example 3.0637And that one is measured, once again, on a logarithmic scale.0643And many others--there are many other logarithmic scales,0646when you have a really, really large pool of information that can be going in as an input,0649but you want to be able to narrow that to a fairly small, manageable, sensible range of values.06530 to 10 is going to have lots of decimals, when you evaluate log of 8 billion and 72 million.0658It is going to have lots of possible decimals to it, but it is going to be a fairly small, manageable number for thinking about.0664Logarithms will also show up in formulas that are analyzing exponential growth,0670because if we are building a formula that is going to be connected to exponential growth,0675if we are trying to break down and figure out what its power is raised,0678we are going to end up having logarithms show up when we are solving it;0682so they will end up showing up in the formula, as well.0684Logarithms show up in formulas for analyzing exponential growth.0686All right, let's get to some examples: A principal investment of 00 is made in an account that compounds quarterly.0690If no further money is deposited, and the account is worth 57.57 in 5 years, what will it be worth after a total of 10 years?“It’s a reasonable question”, agrees Ms Arkcoll, “but I expect the Budget Paper is reflecting the terminology used in TR 2004/16 ­– Income Tax: Plant in residential rental properties.In this ruling, the term “plant” has an extended meaning which covers the full range of depreciable items in a residential property, including loose items of furniture.The car introduced in 2005 was hugely impressive but, at the same time, a little less endearing.If you don’t mind sacrificing a little personality for a while lot of capability, there’s very little that can get close to the M6. Here’s how to pick up a used example that’ll still do the business.




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