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31 Dec 2022, 04:12
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
95% (00:20) correct
5%
(00:12)
wrong
based on 66
sessions
History
Date
Time
Result
Not Attempted Yet
31 Dec 2022, 06:49
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If\( 3^x\)=1/27, then x=?
A. -3
B. -2
C. -1
D. 2
E. 3
Hi all!
At the outset, according to me, if someone has understood just the basic laws of exponents, this question should not trouble.
The level of difficulty should not be intermediate for this question according to me. Its below 600.
If you found it even moderately difficult, please close the concept gaps on exponents soon.
There are two laws I shall use here-
\(x^a\) *\( x^b\) =\( x^a+b\)
\(x^0 \)= 1 (x is not equal to 0 since 0^0 is undefined)
Given,\( 3^x\)=1/27
GMAT Track of thought 1
How do I represent 27 as a power of 3 to be able to set the equation using exponents?
27 = \(3^3\)
So, rewriting this,
\(3^x\) = 1/\(3^3\)
Now, cross-multiply.
\(3^x\) *\( 3^3 \)= 1
GMAT Track of thought 2
Again, I still need to set things up with a common base of 3. What do I do with the 1?
Represent 1 as\( 3^0.\)
So \(3^x\) * \(3^3 \)= \(3^0\)
=>\( 3^(x+3)\)= \(3^0\)
GMAT Track of thought 3
When bases are equal, equate the powers.
=> x+3 = 0
=> x = - 3
Always check before marking the answer. What am I asked? x or x-1 or x+1,..?
Okay, Its x .
So, Option A is the correct answer.
Hope this is clear.
Let me know if you need any help or have any questions as comments/PM.
Devmitra Sen
GMAT Mentor
A. -3
B. -2
C. -1
D. 2
E. 3
Hi all!
At the outset, according to me, if someone has understood just the basic laws of exponents, this question should not trouble.
The level of difficulty should not be intermediate for this question according to me. Its below 600.
If you found it even moderately difficult, please close the concept gaps on exponents soon.
There are two laws I shall use here-
\(x^a\) *\( x^b\) =\( x^a+b\)
\(x^0 \)= 1 (x is not equal to 0 since 0^0 is undefined)
Given,\( 3^x\)=1/27
GMAT Track of thought 1How do I represent 27 as a power of 3 to be able to set the equation using exponents?
27 = \(3^3\)
So, rewriting this,
\(3^x\) = 1/\(3^3\)
Now, cross-multiply.
\(3^x\) *\( 3^3 \)= 1
GMAT Track of thought 2 Again, I still need to set things up with a common base of 3. What do I do with the 1?
Represent 1 as\( 3^0.\)
So \(3^x\) * \(3^3 \)= \(3^0\)
=>\( 3^(x+3)\)= \(3^0\)
GMAT Track of thought 3When bases are equal, equate the powers.
=> x+3 = 0
=> x = - 3
Always check before marking the answer. What am I asked? x or x-1 or x+1,..?
Okay, Its x .
So, Option A is the correct answer.
Hope this is clear.
Let me know if you need any help or have any questions as comments/PM.
Devmitra Sen
GMAT Mentor
31 Dec 2022, 08:52
Kudos
Bookmarks
Bunuel
Key Property: \(\frac{1}{b^n} = b^{-n}\)
So, since \(27 = 3^3\), we know that \(\frac{1}{27} = \frac{1}{3^3}= 3^{-3}\)
Now let's solve the equation.
Given: \(3^x=\frac{1}{27}\)
Substitute: \(3^x = 3^{-3}\), which means \(x = -3\)
Answer: A
