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Dibs
Registered User regular

This is a question from a GMAT practice exam -- I have no idea how they got the answer, and I'm hoping someone here can help me. I tried an online solver and it didn't give me the correct answer, but I know there's some real math geniuses here so I thought I'd give it a shot.

Here is the problem:

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

m = ?

Thoughts? I have asked everyone I know for help here, and we are all drawing a blank.

The correct answer is 35... seems to me (and everyone else) like it should be 17? Is there some rule I'm missing?

Here is the problem:

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

m = ?

Thoughts? I have asked everyone I know for help here, and we are all drawing a blank.

The correct answer is 35... seems to me (and everyone else) like it should be 17? Is there some rule I'm missing?

0

## Posts

Is the equation how PlushyCthulhu wrote it (with the 1/5 power corrected to 18? i.e. (1/4)^m * (1/5)^18 = 2 * (1/10)^35

In any case you solve it using logarithms.

Origin: KafkaAU B-Net: Kafka#1778

Mushiwulfon2) I thought I double checked it, but apparently I still put it in wrong. Here is an image as it is displayed in the practise exam. Mushi was correct, the 1/4 and 1/5 are swapped (but contrary to Cthulu, the 2 is definitely only on the bottom.. or at least that's my understanding).

You can see my guess (solid circle) and the correct answer (squared answer). I am still lost on this.

Sorry for wasting people's time, I feel like an idiot for mistyping it. I knew it was going to be a challenge to get a math problem across properly, but I'm surprised I messed up the simple part.

So, convert (1/4)^18 to 1/(2)^36 (because 4 = 2^2, and (2^2)^18 converts to 2^36). Then multiply both sides of the equation by 2^36. The right side then becomes 2^36/(2(10)^35), which then becomes 2^35/10^35*, which then becomes, (2/10)^35. Thus (1/5)^m = (2/10)^35. 2/10 = 1/5, leaving you with your answer.

* 2^36 divided by 2 is 2^35. Or another way to put it is 2^36/2^1 = 2^(36-1) = 2^35

Hahnsoo1on(1/4)^18 * (1/5)^m = 1/(2*10^35) :given

[(1/2)^2]^18 * (1/5)^m = 1/(2*10^35) : because (1/2)^2 = 1/4

(1/2)^36 * (1/5)^m = 1/(2*10^35) : power rule for exponents

(1/2)^36 * (1/5)^m = 1/(2 * [2^35 * 5^35]) : product rule for exponents

(1/2)^36 * (1/5)^m = 1/(2^36 * 5^35) : multiplying powers of the same base

(1/2)^36 * (1/5)^m = 1/(2^36) * 1/(5^35) : definition of multiplication for fractions

(1^36)/(2^36) * (1^m)/(5^m) = 1/(2^36) * 1/(5^35) : quotient rule for exponents

1/(2^36) * 1/(5^m) = 1/(2^36) * 1/(5^35) : 1^x = 1 for any x != 0

Since both sides are identical except for the variable the variable must be equal to the number occupying its place on the right side.

0431-6094-6446-7088

5^m * 4^18 = 2*10^35

5^m * 4^18 = 2 * 2^35 * 5^35

5^m * 2^36 = 2^36 * 5^35

5^m = 5^35

m = 35