log 4 x = log 16. x log 4 = log 16. The magnitude of an earthquake is a Logarithmic scale. For instance, the base two logarithm of eight is three, because two raised to the power of three equals eight: log 2 8 = 3 because . More examples showing how to simplify logarithms. The famous "Richter Scale" uses this formula: M = log 10 A + B. x log 4 = log 16. Logarithms can be simplified using only one property or a combination of all 3 properties. Answer. Nowadays there are more complicated formulas, but they still use a logarithmic scale. Simplify log 3 40 - log 3 10. In the example above, we use the power property and the product property to simplify log 6 24 + 2 log 6 3. Using natural logs (log e or ln): Carrying all numbers to 5 significant figures, ln 30 = 3.4012 is equivalent to e 3.4012 = 30 or 2.7183 3.4012 = 30 You can divide both sides of the equation by log 4 to get x by itself. There are logarithms using different base units. Remember that log 4 is a number. In this type of log equation, the variable you need to solve for is inside the log, but the equation has more than one log and a constant. The increase from a 4.0 earthquake to a 5.0 quake is tenfold. If you wanted, you could use two as a base unit. You can solve equations with more than one log. Scientists use the Richter scale to compare the seriousness of earthquakes. Exercise #1. Sound . Using log 10 ("log to the base 10"): log 10 100 = 2 is equivalent to 10 2 = 100 where 10 is the base, 2 is the logarithm (i.e., the exponent or power) and 100 is the number. To solve log 2 ( x – 1) + log 2 3 = 5, for instance, first combine the two logs that are adding into one log by using the product rule: Where A is the amplitude (in mm) measured by the Seismograph and B is a distance correction factor. In general, you write log followed by the base number as a subscript. Use a calculator to evaluate the logarithms … 2 3 = 8. 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