Feel the Earth Shake


      Logarithms are used to solve exponential equations because it helps figure out what the coefficient needs to be powered by in order to make the exponential equation true. The reason why logarithms are important when it comes to the studying of earthquakes because they could help simplify the magnitude levels of the earthquake.  Which could be very large are small numbers.

An example would be the following exponential equation:  10^(x+1) = 43

       In order to make this solution to the exponential equations of 43. One must begin with a log base 10 of 43 is equal to x+1. That is to get the power that I need to raise 10 to 7 in order to get to x+1 power to equal 43.

log _{10} 43 = x+1

Next, we need to solve for X and the way an individual would do that is by subtracting one from both sides. To make it easier to solve for X. Minus 1 will be placed outside of the logarithm.

(log _{10} 43 ) – 1 = x + (1 – 1)

(log _{10} 43) – 1= x

Now, this reads as x equals to log base 10 of 43 minus 1.

(log _{10} 43) – 1= x

1.63346845558 – 1 = x

0.63346845558 = x

As you can see when solved x equals 0.63346845558.

When plugged into the exponential equation; 10^(x+1)=43

One will get .43 instead of 43.

Can anyone help me make this equation true?


One Comment Add yours

  1. I found this interesting because I never knew you could use log to calculate the size of an earthquake.


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