In the previous article, we learnt about the basics of logarithms required for GAMSAT. Now we’ll learn some more as well as discuss how to apply what we learnt in the GAMSAT exam.

If you are serious about GAMSAT, then you have grabbed the ACER GAMSAT practice booklets already. If not, you should consider purchasing all the four booklets from ACER website. Let’s take up question 52 of Unit 19 from ACER GAMSAT Blue Book. You’ll see how extensively logarithms and its properties are used in this question. The formula given in the passage is

The question asks for increase in sound intensity, that is the increase in I, when the sound intensity level (β) changes from 60 dB (normal conversation) to 120 dB (threshold of pain). An important property of logarithm is regarding the addition and subtraction of the same.

- log(a*b) = log a + log b
- log(a/b)= log a – log b

Now β/10=log (I)-log (10^{-12}) means that 6 = log (I_{1})-log (10^{-12}) for normal conversation and 12 = log (I_{2})-log (10^{-12}) for threshold of pain

From the two equations, you can easily deduce the direct relation between I_{1} and I_{2} as follows:

log (I_{2}) – log (I_{1}) = 12 – 6

or log(I_{2}/ I_{1}) = 6. From the definition of logarithms and taking the base as 10, I_{2}/ I_{1 }= 10^{6} which gives you C as the answer. So you see how important it is to understand and master the principles of logarithms and exponents. Some other useful properties of logarithms are

- log 1 = 0
- log
_{a}a = 1 - log
_{a}b^{k }= k log_{a}b - log
_{a}b = log_{a}c × log_{c}b - log
_{a}b × log_{b}a = 1

**What is Natural Log?**

Natural logarithm is the same as other logarithmic functions, except that the base is **e,** which has a value of 2.72. Natural log isn’t much different from general logarithm and all the above discussed properties hold good for natural logs as well. Natural log is important because many formulas in chemistry and physics are in terms of natural logs. You can convert the natural log into Base 10 logarithms using the following formula:-

ln a = 2.3 × log_{10}a

Source: patrickjmt.com