Reading Logarithms

One way to conceptualize logarithms is as a tool to quantify exponential growth or decay of an object in a system. They offer a unique perspective on exponential relationships. Consider this equation:

$2^7 = 128$

Here, in the logarithmic view, '2' is the growth rate. '7' is the time. And, '128' is the final state of growth, given that an object has been growing doubly for a duration of 7 units.

$2^0 = 1$

Here, another object wants to grow doubly but the '0' time says that the growth process hasn't begun. Therefore, the size has remained whole or 100% of its original size, as indicated by the '1'.

$2^{-1} = \frac{1}{2}$

Here, the negative sign in the time '-1' means a past event, i.e. going backward in time in the growth. The result '1/2' means that the size of the object was half its original size. Since, it was meant to grow doubly at each step of the time, it is halved. Its size would have been one-third the original size, if it was growing triply, a quarter of the original size if it grew quadruply and so on.

These equations, can be represented using the logarithms as below.

$2^7 = 128 \rightarrow \log_2 128 = 7$ $2^0 = 1 \rightarrow \log_2 1 = 0$ $2^{-1} = \frac{1}{2} \rightarrow \log_2 \frac{1}{2} = -1$