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

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

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New post 14 Jun 2017, 02:36
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Re: If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

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New post 14 Jun 2017, 02:39
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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
x = 4/3. Answer A...
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Re: If (–3)^(2x) = 3^(4 – x), what is the value of x?  [#permalink]

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New post 14 Jun 2017, 04:16
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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New post 14 Jun 2017, 06:58
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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New post 15 Jun 2017, 15:27
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.

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

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New post 11 Sep 2018, 00:13
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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