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Senior Manager  V
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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

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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, 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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Posts: 3573
Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

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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

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

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

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

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

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

$$3=7x$$

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

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Senior Manager  V
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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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Oh yes. I tried a lot actually but i couldn't do it perfectly as i am new here. Thanks for correcting _________________
Why do we fall?...So we can learn to pick ourselves up again
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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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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!
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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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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 ?
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If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?  [#permalink]

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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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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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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If (0.1)^-(x-1) = (0.0001)^x/3, then what is the value of x?   [#permalink] 03 Oct 2018, 17:35
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