GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Jun 2019, 18:05

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If (–3)^(2x) = 3^(4 – x), what is the value of x?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 55670
If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

### Show Tags

14 Jun 2017, 03:36
00:00

Difficulty:

15% (low)

Question Stats:

84% (01:17) correct 16% (01:36) wrong based on 102 sessions

### HideShow timer Statistics

If $$(–3)^{2x} = 3^{(4 – x)}$$, what is the value of x?

A. 4/3
B. 1
C. 4
D. –1
E. 0

_________________
Director
Joined: 04 Dec 2015
Posts: 740
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

### Show Tags

14 Jun 2017, 03:39
3
Bunuel wrote:
If $$(–3)^{2x} = 3^{(4 – x)}$$, what is the value of x?

A. 4/3
B. 1
C. 4
D. –1
E. 0

$$(–3)^{2x} = 3^{(4 – x)}$$
$$(3)^{2x} = 3^{(4 – x)}$$
2x = 4 - x
3x = 4
Manager
Joined: 17 Feb 2016
Posts: 90
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q47 V36
GPA: 3.12
WE: Education (Internet and New Media)
Re: If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

### Show Tags

14 Jun 2017, 05:16
Here -3^2x is always positive so is equal to 3^2x
2x=4-x
x=4/3
_________________
Never stop fighting until you arrive at your destined place - that is, the unique you. Have an aim in life, continuously acquire knowledge, work hard, and have the perseverance to realise the great life. A. P. J. Abdul Kalam
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4504
Location: India
GPA: 3.5
If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

### Show Tags

14 Jun 2017, 07:58
1
Bunuel wrote:
If $$(–3)^{2x} = 3^{(4 – x)}$$, what is the value of x?

A. 4/3
B. 1
C. 4
D. –1
E. 0

$$(–3)^{2x} = 3^{(4 – x)}$$

Or, $$(–1)^{2x}*(3)^{2x} = 3^{(4 – x)}$$

$$(–1)^{2x}$$ will result in 1 , as it is has got an even power...

Now, $$(3)^{2x} = 3^{(4 – x)}$$

Or, $$4 - x = 2x$$

Or, $$3x = 4$$

So, $$x = \frac{4}{3}$$

Thus, answer will be (A) $$\frac{4}{3}$$
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6567
Location: United States (CA)
Re: If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

### Show Tags

15 Jun 2017, 16:27
Bunuel wrote:
If $$(–3)^{2x} = 3^{(4 – x)}$$, what is the value of x?

A. 4/3
B. 1
C. 4
D. –1
E. 0

We can see that the bases, -3 and 3, are opposites. In such a case, if x ≠ 1 and (-x)^a = x^b, then the exponents a and b are equal if the exponents are even integers or fractions (in lowest terms) with even numerators.

Here, we have (-3)^(2x) = 3^(4 - x). Let’s assume the exponents are equal, that is, we have 2x = 4 - x (we have to verify that the exponents are either even integers or fractions with even numerators after we’ve solved for x):

2x = 4 - x

3x = 4

x = 4/3

Thus, the exponent of -3 is 2x = 2(4/3) = 8/3 and that of 3 is 4 - x = 4 - 4/3 = 8/3. As we can see, 8/3 is a fraction with an even numerator. Thus, x = 4/3.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3373
Location: India
GPA: 3.12
If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

### Show Tags

11 Sep 2018, 01:13
Bunuel wrote:
If $$(–3)^{2x} = 3^{(4 – x)}$$, what is the value of x?

A. 4/3
B. 1
C. 4
D. –1
E. 0

This problem tests an important property: An even power of any number is always positive

In this case, we have $$(-3)^2 = 3^2$$ -> $$(–3)^{2x} = (3)^{2x}$$. Our equation becomes $$(3)^{2x} = 3^{(4 – x)}$$

As we have a common base on both sides, we get $$2x = 4 - x$$ -> $$3x = 4$$

Therefore, the value of x is $$\frac{4}{3}$$(Option A)
_________________
You've got what it takes, but it will take everything you've got
If (–3)^(2x) = 3^(4 – x), what is the value of x?   [#permalink] 11 Sep 2018, 01:13
Display posts from previous: Sort by