Solve the following equation for 'm':

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

I don't remember how to solve this, and I need help. A step by step solution would be very helpful.

Thanks!

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- Jan 25th 2011, 12:53 PMmrtontoHelp with solving exponential equation
Solve the following equation for 'm':

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

I don't remember how to solve this, and I need help. A step by step solution would be very helpful.

Thanks! - Jan 25th 2011, 01:02 PMpickslides

so

- Jan 25th 2011, 03:17 PMmrtonto
So here's the thing: I have been out of school for several years, and I'm thinking about going back to get a Master's Degree. I was taking a practice GMAT test and this was one of the questions. I can do this problem with a calculator, but I am supposed to be able to do this by hand for the test. I understand everything you've done so far, but I still don't know how to do this by hand. I am pretty sure once I see this worked out that it will come back to me.

- Jan 25th 2011, 03:22 PMpickslides
I have done it all bar the last step.

It is taking of both sides. - Jan 25th 2011, 03:34 PMHallsofIvy
and so you can write everything on the right as powers of 2 and 5.

Do it! You'll like it! - Jan 25th 2011, 03:35 PMskeeter

- Jan 26th 2011, 09:21 AMmrtonto
Thanks so much for the help. You guys are the best!

- Jan 27th 2011, 11:14 AMinternetimm28
1/5)^m = 1/5^m, and (1/4)^18 = 1/4^18 (since 1 raised to any power = 1)

Additionally, 4^18 = (2^2)^18 = 2^36.

Since both sides of the equation have 1 in the their numerators, to set them = we have to set the demoninators equal to each other.

The denominator of the left side is now = 5^m*2^36

The denominator of the right side = 2(10)^35, which can be rewritten as (2)(2*5)^35, or (2)(2^35)(5^35).

Since (2)(2^35)= 2^36, 2^36 can be cancelled from each side of the equation. We are now left with 5^m = 5^35. m = 35, and the correct answer is D :D

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