GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 06 Jul 2020, 02:04 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?

Author Message
TAGS:

### Hide Tags

SC Moderator V
Joined: 25 Sep 2018
Posts: 872
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)
If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

### Show Tags

2
3 00:00

Difficulty:

(N/A)

Question Stats: 59% (01:50) correct 41% (02:13) wrong based on 59 sessions

### HideShow timer Statistics

If $$(0.1)^{-(x-1)} = (0.0001)^{\frac{x}{3}}$$, then what is the value of x?

A) 4

B) 3

C) $$\frac{3}{7}$$

D) 0

E) $$\frac{-3}{7}$$

_________________

Originally posted by Abhi077 on 28 Sep 2018, 07:41.
Last edited by generis on 28 Sep 2018, 09:49, edited 2 times in total.
Renamed the topic and edited the question. Formatted the question.
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3940
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

### Show Tags

3
1
Abhi077 wrote:
If $$(0.1)^-x-1$$ =$$(0.0001)^\frac{x}{3}$$, then what is the value of x?

A)4
B)3
C)$$\frac{3}{7}$$
D)0
E)$$\frac{-3}{7}$$

Some formatting issues. These exponents are hard! I think you mean:

$$(0.1)^{-(x-1)}=(0.0001)^{\frac{x}{3}}$$

Make bases equal, then set exponents equal

$$(10^{-1})^{-(x-1)}=(10^{-4})^{\frac{x}{3}}$$

$$(10^{-1})^{(-x+1)}=(10^{-1})^{(4*\frac{x}{3})}$$

$$(10^{-1})^{(-x+1)}=(10^{-1})^{\frac{4x}{3}}$$

$$-x+1=\frac{4x}{3}$$

$$-3x+3=4x$$

$$3=7x$$

$$x=\frac{3}{7}$$

_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.

BLACK LIVES MATTER.
SC Moderator V
Joined: 25 Sep 2018
Posts: 872
Location: United States (CA)
Concentration: Finance, Strategy
GPA: 3.97
WE: Investment Banking (Investment Banking)
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

### Show Tags

1
Oh yes. I tried a lot actually but i couldn't do it perfectly as i am new here. Thanks for correcting _________________
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3940
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

### Show Tags

1
Abhi077 wrote:
Oh yes. I tried a lot actually but i couldn't do it perfectly as i am new here. Thanks for correcting Not to worry. I commend you for the attempt, which is impressive for someone new.

We need {curly brackets} around any exponent that is not 0 or positive 1-9.

One way to figure out formatting is to "peek" at others' formatting.

In this case, for example you could
1) screenshot my post to record the polished version, then
2) click "reply" on my post. Doing so will reveal the codes I entered. Take another screenshot. Then choose "cancel" or close the tab. Your fake "reply" will not post. Welcome to GMAT Club!
_________________
Visit SC Butler, here! Get two SC questions to practice, whose links you can find by date.

Our lives begin to end the day we become silent about things that matter. -- Dr. Martin Luther King, Jr.

BLACK LIVES MATTER.
VP  D
Joined: 09 Mar 2016
Posts: 1252
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

### Show Tags

generis wrote:
Abhi077 wrote:
If $$(0.1)^-x-1$$ =$$(0.0001)^\frac{x}{3}$$, then what is the value of x?

A)4
B)3
C)$$\frac{3}{7}$$
D)0
E)$$\frac{-3}{7}$$

Some formatting issues. These exponents are hard! I think you mean:

$$(0.1)^{-(x-1)}=(0.0001)^{\frac{x}{3}}$$

Make bases equal, then set exponents equal

$$(10^{-1})^{-(x-1)}=(10^{-4})^{\frac{x}{3}}$$

$$(10^{-1})^{(-x+1)}=(10^{-1})^{(4*\frac{x}{3})}$$ how ?
$$(10^{-1})^{(-x+1)}=(10^{-1})^{\frac{4x}{3}}$$

$$-x+1=\frac{4x}{3}$$

$$-3x+3=4x$$

$$3=7x$$

$$x=\frac{3}{7}$$

$$(10^{-1})^{(-x+1)}=(10^{-1})^{(4*\frac{x}{3})}$$ how ?
Director  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 950
WE: Supply Chain Management (Energy and Utilities)
If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

### Show Tags

1
dave13 wrote:
generis wrote:
Abhi077 wrote:
If $$(0.1)^-x-1$$ =$$(0.0001)^\frac{x}{3}$$, then what is the value of x?

A)4
B)3
C)$$\frac{3}{7}$$
D)0
E)$$\frac{-3}{7}$$

Some formatting issues. These exponents are hard! I think you mean:

$$(0.1)^{-(x-1)}=(0.0001)^{\frac{x}{3}}$$

Make bases equal, then set exponents equal

$$(10^{-1})^{-(x-1)}=(10^{-4})^{\frac{x}{3}}$$

$$(10^{-1})^{(-x+1)}=(10^{-1})^{(4*\frac{x}{3})}$$ how ?
$$(10^{-1})^{(-x+1)}=(10^{-1})^{\frac{4x}{3}}$$

$$-x+1=\frac{4x}{3}$$

$$-3x+3=4x$$

$$3=7x$$

$$x=\frac{3}{7}$$

$$(10^{-1})^{(-x+1)}=(10^{-1})^{(4*\frac{x}{3})}$$ how ?

Exponent property:-
$$(a^m)^n=a^{m*n}=(a^n)^m$$

Here, we can write $$(10^{-4})^{\frac{x}{3}}$$ as $$(10^{(-1)*(4)})^{\frac{x}{3}}$$ or,
$$(10^{(-1)})^{\frac{4*x}{3}}$$
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 11036
Location: United States (CA)
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

### Show Tags

Abhi077 wrote:
If $$(0.1)^{-(x-1)} = (0.0001)^{\frac{x}{3}}$$, then what is the value of x?

A) 4

B) 3

C) $$\frac{3}{7}$$

D) 0

E) $$\frac{-3}{7}$$

As with most exponential equations, we will re-express the expressions on each side of the equation with a common base. In this case, the base is 10. We can then set the exponents equal to each other and solve for x.

(0.1)^-(x -1) = (0.0001)^(x/3)

(10^-1)^-(x -1) = (10^-4)^(x/3)

10^(x - 1) = 10^(-4x/3)

x - 1 = -4x/3

7x/3 = 1

x = 3/7

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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

Director  D
Joined: 12 Dec 2015
Posts: 524
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

### Show Tags

Abhi077 wrote:
If $$(0.1)^{-(x-1)} = (0.0001)^{\frac{x}{3}}$$, then what is the value of x?

A) 4

B) 3

C) $$\frac{3}{7}$$ --> correct

D) 0

E) $$\frac{-3}{7}$$

Calculation:
$$(0.1)^{-(x-1)} = (0.0001)^{\frac{x}{3}}$$
=> $$(10)^{(x-1)} = (10^{-4})^{\frac{x}{3}}$$
=> $$(10)^{(x-1)} = (10)^{\frac{-4x}{3}}$$
=> x-1 = -4x/3
=> 3x -3 = -4x
=> 7x=3
=> x = 3/7 Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?   [#permalink] 02 Nov 2019, 07:47

# If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  