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use of mathematics – to design complex gears,analyse the stability of bridges and buildings, and construct cars, lorries, ships, and aeroplanes. Logarithms were a firm part of the school mathematics curriculum a few decades ago. And engineers carried what was in effect an analogue calculator for logarithms in their pockets, a physical representation of the basic equation for logarithms for on-the-spot use. They called it a slide rule, and they used it routinely in applications ranging from architecture to aircraft design.
    The first slide rule was constructed by an English mathematician, William Oughtred, in 1630, using circular scales. He modified the design in 1632, by making the two rulers straight. This was the first slide rule. The idea is simple: when you place two rods end to end, their lengths add. If the rods are marked using a logarithmic scale, in which numbers are spaced according to their logarithms, then the corresponding numbers multiply . For instance, set the 1 on one rod against the 2 on the other. Then against any number x on the first rod, we find 2x on the second. So opposite 3 we find 6, and so on, see Figure 11 . If the numbers are more complicated, say 2.67 and 3.51, we place 1 opposite 2.67 and read off whatever is opposite 3.59, namely 9.37. It’s just as easy.

    Fig 11 Multiplying 2 by 3 on a slide rule.
    Engineers quickly developed fancy slide rules with trigonometric functions, square roots, log-log scales (logarithms of logarithms) to calculate powers, and so on. Eventually logarithms took a back seat to digital computers, but even now the logarithm still plays a huge role in science and technology, alongside its inseparable companion, the exponential function. For base-10 logarithms, this is the function 10 x ; for natural logarithms, the function e x , where e = 2.71828, approximately. In each pair, the two functions are inverse to each other. If you take a number, form its logarithm, and then form the exponential of that, you get back the number you started with.
    Why do we need logarithms now that we have computers?
    In 2011 a magnitude 9.0 earthquake just off the east coast of Japancaused a gigantic tsunami, which devastated a large populated area and killed around 25,000 people. On the coast was a nuclear power plant, Fukushima Dai-ichi (Fukushima number 1 power plant, to distinguish it from a second nuclear power plant situated nearby). It comprised six separate nuclear reactors: three were in operation when the tsunami struck; the other three had temporarily ceased operating and their fuel had been transferred to pools of water outside the reactors but inside the reactor buildings.
    The tsunami overwhelmed the plant’s defences, cutting the supply of electrical power. The three operating reactors (numbers 1, 2, and 3) were shut down as a safety measure, but their cooling systems were still needed to stop the fuel from melting. However, the tsunami also wrecked the emergency generators, which were intended to power the cooling system and other safety-critical systems. The next level of backup, batteries, quickly ran out of power. The cooling system stopped and the nuclear fuel in several reactors began to overheat. Improvising, the operators used fire engines to pump seawater into the three operating reactors, but this reacted with the zirconium cladding on the fuel rods to produce hydrogen. The build-up of hydrogen caused an explosion in the building housing Reactor 1. Reactors 2 and 3 soon suffered the same fate. The water in the pool of Reactor 4 drained out, leaving its fuel exposed. By the time the operators regained some semblance of control, at least one reactor containment vessel had cracked, and radiation was leaking out into the local environment. The Japanese authorities evacuated 200,000 people from the surrounding area because the radiation was well above normal safety limits. Six months later, the company operating the reactors, TEPCO, stated that the situation