00:01
In the given question, we are told to use the richer scale which is given as r is equal to log of i divided by i 0.
00:13
And we are told to find the intensity of an earthquake.
00:18
The intensity i over here gives us the intensity of an earthquake.
00:24
So i is intensity.
00:25
Intensity of an earthquake measuring r on the richer scale and we are told to take i0 as 1 and now the first value that is being given to us is r which is given as 7 .8 and we have to find the corresponding i value for this richer scale value of 7 .8 so using the the formula we can write 7 .8 is then equal to log of i by i0.
01:01
Since we took i0 equal to 1, we can write log of i.
01:06
Now there is a property that we can use over here, which is that when we take 10 to the power of log of a certain number or let's say a variable, we would get the result of this expression as the expression that we have inside the logarithm.
01:24
Over here it is c, so what we have as the result of 10 to the power of log c is c.
01:31
So we will take each side of this equation as powers of 10 and then what we would have is that i is equal to 10 point 10 raised to the power of 7 .8.
01:48
So now we can just use a calculator to find the value when 10 is raised to the power of 7 .8 and this would give us the value of i to be equal to to be equal to 6 .31 times 10 to the power of 7 so this is what we would have we would have as the intensity of the earthquake and we are told to round our answers to the nearest whole number, right? so for rounding it to the nearest whole number, we would have to write this number as the exact number is 63095734 .4 and this would be the required answer...