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Math Expert V
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If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

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

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

A. 4/3
B. 1
C. 4
D. –1
E. 0

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Director  V
Joined: 04 Dec 2015
Posts: 740
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Re: If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

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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
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Re: If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

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Here -3^2x is always positive so is equal to 3^2x
2x=4-x
x=4/3
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If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

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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) $$\frac{4}{3}$$
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Re: If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

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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.

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

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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)
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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
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