Problem Solving

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

what is m?


please help me, how do you find this?

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

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 ?