Saheed Busayo Akanni Probably because the range is too large to be shown easily and clearly on a linear axis. Logarithms will compress the data. Consider trying to show $1, $100, $1 million, $1 billion dollars on a linear axis. Consider the same situation with logarithms.

@Alan F Rawle thanks so much for your quick response. You are highly appreciated Prof. Blessings!

In the financial markets, agents are normally interested in knowing the return on assets in percentage terms. On the logarithmic scale, the distance between one point and another is a % of the total, unlike the linear scale, which represents monetary units.

Imagine you bought two shares: one for $5.00 and sold it for $10.00, and one for $50.00 and sold it for $55.00. On the linear scale, the gain was the same, that is, 5 monetary units.

On a logarithmic scale, in the first case the return on the operation was 100%, while in the second, it yielded 10%.

@Adriano Filipe da Silva Maia thanks for your comprehensive explanations Prof. I really appreciate you. Blessings!!

ceteris paribus = "other things being equal"

In the light of Adriano Filipe da Silva Maia's answer:

and as many textbooks used to say:

If investors require a 14% per annum expected return when the stock price is $10, then, ceteris paribus, they will also require a 14% per annum expected return when it is $50.

So, obviously, the assumption of constant expected drift (change) rate is inappropriate and needs to be replaced by the assumption that the expected return (i.e., expected drift (change) divided by the stock price) is constant.

Now, Saheed Busayo Akanni, just translate (rewrite) the last (above) sentence in math formulas = as an equation:

that is, if S is the stock price at time t, i.e., S is a function of t, S(t), then the equation is delta(S)/S = mu*delta(t). Integration of the last one (expression/ equation) from time 0 to T yields the log-return ln( S(T)/S(0) ) = mu*T, where constant 'mu' is the expected rate of return on the stock. (btw, this means that in a short interval of time, delta(t), the expected increase in S is mu*S*delta(t).)

Furthermore,

https://www.google.com/search?q=log+returns+are+additive

https://www.google.com/search?q=log+returns+are+normally+distributed

perhaps, there are few other advantages as well ...

Log-returns are used in financial time series modelling for the distribution of log-returns and can be projected to any horizon, unlike linear returns.

Log-returns typically have a symmetric distribution which makes modelling easier.

Log-returns are additive, which means that the k-period log-return is the sum of the k one-period log-returns.