The magnitude of an earthquake is a Logarithmic scale. In the example above, we use the power property and the product property to simplify log 6 24 + 2 log 6 3. Exercise #1. The increase from a 4.0 earthquake to a 5.0 quake is tenfold. 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: Bankers use natural logarithms to calculate the time required for a sum of money deposited at an interest rate to reach the desired balance. If you wanted, you could use two as a base unit. Scientists use the Richter scale to compare the seriousness of earthquakes. log 4 x = log 16. x log 4 = log 16. 2 3 = 8. Use the power property of logarithms to simplify the logarithm on the left side of the equation. More examples showing how to simplify logarithms. Nowadays there are more complicated formulas, but they still use a logarithmic scale. 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. Sound . x log 4 = log 16. In general, you write log followed by the base number as a subscript. 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. Simplify log 3 40 - log 3 10. You can solve equations with more than one log. You can divide both sides of the equation by log 4 to get x by itself. Remember that log 4 is a number. The famous "Richter Scale" uses this formula: M = log 10 A + B. 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 . There are logarithms using different base units. Where A is the amplitude (in mm) measured by the Seismograph and B is a distance correction factor. 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 Logarithms can be simplified using only one property or a combination of all 3 properties. Use a calculator to evaluate the logarithms … Answer.

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