Algebra Strategy Guide, Chp. 3 - Exponents

[clarence.booth]

Hi,

I need help on solving the following problem in the Alg. Strat, Guide in Chp. 3, pg. 45:

#9. If m and n are positive integers and (2^18)(5^m) = (20^n), what is the value of m?

Thanks in advance for the help.

Clarence

[anshul04]

This can be solved easily by simplifying the given equation, as shown below:

(2^18)(5^m) = (20^n)
(2^18)(5^m) = (2 x 2 x 5)^n
(2^18)(5^m) = (2^2 x 5)^n
(2^18)(5^m) = (2^(2n)) (5^n)

When we are at this point (means - same bases, 2 & 5, on either side of equation), the respective exponents on either side should also match. That is,
18 = 2n, and m = n

Solving this gives us m = n = 9.

[tim]

Thanks, Anshul! Let us know if there are any further questions on this one.

[RonPurewal]

This can be solved easily

Though you probably didn't intend it this way, your use of "easily" (which I've noticed in your other postings, too) is likely to be insulting to the original poster, to whom this obviously wasn't "easy".

Helpful user contributions are always welcome on the math forum, but please keep in mind that people are posting here in the first place because they can't "easily" solve the problems.

[anshul04]

This can be solved easily

Though you probably didn't intend it this way, your use of "easily" (which I've noticed in your other postings, too) is likely to be insulting to the original poster, to whom this obviously wasn't "easy".

Helpful user contributions are always welcome on the math forum, but please keep in mind that people are posting here in the first place because they can't "easily" solve the problems.

Although I never had any intention to insult anybody here (or anywhere, for that matter), your point is still well taken. I'll be more careful of "my selection" of words in future so that people don't take my statements with unintended meaning.

[tim]

Thanks, and we look forward to further contributions from you on the forum!

[RonPurewal]

Although I never had any intention to insult anybody here (or anywhere, for that matter), your point is still well taken. I'll be more careful of "my selection" of words in future so that people don't take my statements with unintended meaning.

Yeah. Understood that it wasn't intended that way—most likely, you just never thought about it from that angle at all. No worries.

This test is a deeply emotional thing for lots of aspirants, so it's best to keep the vibe as encouraging as possible.

Thanks for visiting!

[clarence.booth]

Anshul, thanks for the help. Your explanation on a previous problem (#8) helped with the approach on this problem (#9):

"For most of the problems involving exponents, I normally take one basic approach - simplify the given equation / expression to consolidate common base(s) (by adding / subtracting / multiplying exponents) so that I have the given expression / equation in its most simplified form. Once I have that, it's just a matter of few seconds to figure out the right answer."

Same thing here: set bases and exponents equal to each other on both sides by simplifying the equation.

The light bulb turned on!

CB

[tim]

:)