Logarithm Operation Explained (2)

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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_kD^m is equivalent to mlog_kD.
With 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:
log₁₀ 0.5 = log₁₀10^y 
-0.301      = y  log₁₀10
-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.

log₅ (0.5) = log₅ 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