Monday, 23 November 2009

Logarithm Operation Explained (2)

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 10y or 5y ?

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

The application requires the Power rule that states that logkDm is equivalent to mlogkD.
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 = 10y

Performing "log" on both sides:
log10 0.5 = log1010y 
-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 = 5y
Here we just "log" to base 5.

log5 (0.5) = log5 5y = 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.


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