Given that 90 is a little less than 100, and 100 equals 102, it seems like 90 should equal 10 raised to some number slightly less than 2. But raised to what number, exactly? Logarithms were invented to answer such questions. On a calculator, if you type in 90 and then press the log button, you get log 90 = 1.9542 . . . . That’s the answer: 101.9542 . . . = 90. In this way, logarithms enable us to write any positive number as a power of ten. Doing that makes many calculations easier and also reveals surprising connections between numbers. Look what happens if we multiply 90 by a factor of
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