Logarithm operator exists as a mathematical tool to allow us to convert a number to another form in terms of base and power.

Can you make 0.5 in terms of 10

^{y}or 5

^{y }?

The above is a maths question that can use logarithm to solve.

The application requires the Power rule that states that

**log**.

_{k}D^{m}is equivalent to mlog_{k}DWith that knowledge, to convert the above question of 0.5 to various base, we simply log the 0.5 to its respecive base.

Let's go for the base 10.

Original: 0.5 = 10

^{y}

Performing "log" on both sides:

**log**0.5 =

_{10}**log**10

_{10}^{y}

-0.301 = y log

_{10}10

-0.301 = y

or another way to put the outcome is

**0.5 = 10**

^{-0.301}We have managed to convert the original number of 0.5 to one with base 10 and a power (index) of "-0.301".

We can also similarly do the same for a base of 5. => 0.5 = 5

^{y}

Here we just "log" to base 5.

**log**(0.5) =

_{5}**log**5

_{5}^{y }= y

-0.431 = y

Thus

**0.5 = 5**

^{-0.431}From the 2 examples above, you can see the wonders of having logarithm as a conversion tool.

Once you understand this principles, you will appreciate logarithm.

Cheers!

:D

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