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GMAT Prep exponent help!

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Source: — Problem Solving |
Master | Next Rank: 500 Posts
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by krisraam » Tue Feb 03, 2009 5:46 pm
1/5^m * 1/ 4^18 = 1/(2*10^35)

==> 1/5^m * 1/ 2^36 = 1/ 1/(2* 2^35 * 5^35)

==> 1/5^m = 1/5^35 ( Cancel out 2^36 on both sides)

==> 5^m = 5^35

==> m = 35

Thanks
Raama
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Junior | Next Rank: 30 Posts
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by dimonya » Tue Feb 03, 2009 9:50 pm
in general to solve such equation we need to use logarithms!

1/5^m * 1/ 4^18 = 1/(2*10^35)

take natural logarithm of both sides to get

m(ln5)+18(ln4)=ln2+35ln10

m(ln5)=ln2+35ln10-18(ln4)

m=(ln2+35ln10-18ln4)/ln5


every decent calculator has a tool for calculating natural logarithms

evaluating the last expression yields m=35

might seem hard, but if the equation gets a bit less obvious its is way easier to just use logarithms.


BTW are we allowed to use some sort of calculator on the test ?
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