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

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Manager
Joined: 25 Sep 2018
Posts: 117
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
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WE: Investment Banking (Investment Banking)
If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

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Updated on: 28 Sep 2018, 09:49
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45% (medium)

Question Stats:

60% (01:37) correct 40% (02:22) wrong based on 43 sessions

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

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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.
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Joined: 22 May 2016
Posts: 2204
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

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28 Sep 2018, 08:39
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

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

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

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

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

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

$$3=7x$$

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

Manager
Joined: 25 Sep 2018
Posts: 117
Location: United States (CA)
Concentration: Finance, Strategy
GMAT 1: 640 Q47 V30
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]

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28 Sep 2018, 08:45
1
Oh yes. I tried a lot actually but i couldn't do it perfectly as i am new here. Thanks for correcting
_________________

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Joined: 22 May 2016
Posts: 2204
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

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28 Sep 2018, 09:40
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!
VP
Joined: 09 Mar 2016
Posts: 1215
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

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01 Oct 2018, 13:09
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
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

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01 Oct 2018, 18:42
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,
$$(10^{(-1)})^{\frac{4*x}{3}}$$
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Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

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03 Oct 2018, 16:35
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

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Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x? &nbs [#permalink] 03 Oct 2018, 16:35
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