Thursday, April 23, 2015

Find the value $12^\frac{1-(x+y)}{2(1-y)}$ given $3=60^x$ and $5=60^y$.

Without using the calculator and the help from logarithm, evaluate $\large12^\frac{1-(x+y)}{2(1-y)}$ if $3=60^x$ and $5=60^y$.

Aww, this problem looks easy peasy if we could solve it using the logarithm method as we can convert the exponential forms to logarithmic forms and get:

$\log_{60}3=x$ and $\log_{60}5=y$

Adding them up gives


Algebraically manipulating the above so we have








Divide (*) by (**) we have:


Convert this logarithm form into the exponential form again we have what we are desired:


But, the question is, we are not allowed to solve using the help from logarithm method.

Now, take out a pencil, or a pen, to start scribble, this problem provides you the golden opportunity that you simply cannot pass up as this problem will promote you to think logically, abstractly, critically and creatively.

As usual, I will show you how I tackle the problem in my next blog post, see you!

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