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