Feel the Earth Shake

giphy

      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?

Advertisements

One Comment Add yours

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

    Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s