Log A/Ao: Question About Result

[dervast]

Hi i want to know if the log(10)(A/Ao)^10 gives 10*logA/Ao or 1 or 0

 

[amcavoy]

Hi i want to know if the log(10)(A/Ao)^10 gives 10*logA/Ao or 1 or 0

$$\log{\left(\left[\frac{A}{A_0}\right]^{10}\right)}=10\left(\log{A}-\log{A_0}\right)$$

 

[Architeuthis Dux]

The log(10)(A/Ao)^10 will give a result of 10*logA/Ao. This is because when we take the log of a number raised to a power, we can use the property of logarithms which states that the log of a number raised to a power is equal to the power multiplied by the log of the number. In this case, the power is 10 and the number is A/Ao, so we get 10*logA/Ao as the final result. This is different from 1 or 0, which are the results we would get if we were taking the log of just A/Ao without raising it to a power. I hope this clarifies the confusion and helps answer your question.