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655-705 Level|   Exponents|      
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Abhi077
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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x? Updated on: 28 Sep 2018, 10:49
Originally posted by Abhi077 on 28 Sep 2018, 08:41.
Last edited by generis on 28 Sep 2018, 10:49, edited 2 times in total.
Renamed the topic and edited the question. Formatted the question.
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Difficulty:

55% (hard)

Question Stats:

59% (01:55) correct 41% (02:07) wrong based on 113 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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C
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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x? 28 Sep 2018, 09:39
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Abhi077
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

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

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

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

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

\(-3x+3=4x\)

\(3=7x\)

\(x=\frac{3}{7}\)

Answer C
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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x? 28 Sep 2018, 09:45
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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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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x? 28 Sep 2018, 10:40
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Abhi077
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!
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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x? 01 Oct 2018, 14:09
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generis
Abhi077
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 ?
\((10^{-1})^{(-x+1)}=(10^{-1})^{\frac{4x}{3}}\)

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

\(-3x+3=4x\)

\(3=7x\)


\(x=\frac{3}{7}\)

Answer C




\((10^{-1})^{(-x+1)}=(10^{-1})^{(4*\frac{x}{3})}\) how ?
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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x? 01 Oct 2018, 19:42
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dave13
generis
Abhi077
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 ?
\((10^{-1})^{(-x+1)}=(10^{-1})^{\frac{4x}{3}}\)

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

\(-3x+3=4x\)

\(3=7x\)


\(x=\frac{3}{7}\)

Answer C




\((10^{-1})^{(-x+1)}=(10^{-1})^{(4*\frac{x}{3})}\) 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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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x? 03 Oct 2018, 17:35
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Abhi077
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

Answer: C
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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x? 02 Nov 2019, 08:47
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Abhi077
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
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