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If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?

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If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]

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New post 27 Nov 2017, 23:18
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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]

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New post 28 Nov 2017, 00:51
3^4*10^4= 3^6x
Take root of both side
900=3^3x...equ1

Now we have to solve for (3^(x-1))^3= (3^3x)/3^3 ....equ2
From equation 1 and 2, answer is 100/3.
"B"

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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]

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New post 28 Nov 2017, 02:41
3^6x = 810,000;
3^3x = (810,000)^1/2 = 900

3^(3x-3)= (900/3^3) = 100/3

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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]

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New post 28 Nov 2017, 04:44
Given \(3^(6x) = 810,000\)
which is simplified as

\((3^(3x))^2=9^2 * 10^4\)

\(3^(3x) = 9 * 10^2\)=\(3^2*10^2\)

hence, \((3^(x-1))^3=((3^x)/3)^3=3^(3x)/3^3\)
=\((3^2 * 10^2)/(3^3)\)
=100/3

Answer: 100/3

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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]

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New post 28 Nov 2017, 06:04
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Bunuel wrote:
If \(3^{(6x)} = 810,000\), what is the value of \((3^{(x−1)})^3\)?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300




\((3^{x−1})^3 = 3^{3x}/27\)

We know
\(3^{6x} = 810,000\)
So \(3^{3x} = 900\) (taking square root on both sides)

We get \(3^{3x}/27 = 900/27 = 100/3\)

Answer (B)
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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3? [#permalink]

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New post 29 Nov 2017, 18:13
Bunuel wrote:
If \(3^{(6x)} = 810,000\), what is the value of \((3^{(x−1)})^3\)?

A. 10/3

B. 100/3

C. 200/3

D. 150

E. 300


Let’s first re-express (3^(x - 1))^3, noting that when we have an exponent raised to an exponent, we multiply the two exponents. Thus, (3^(x - 1))^3 = 3^(3x - 3) = (3^3x)(3^-3) = (3^3x)/(3^3), so really we need to determine the value of 3^3x/27.

Simplifying the given equation, we have:

3^6x = 810,000

Taking the square root of both sides, we have:

3^3x = 900

Thus, (3^3x)/(27) = 900/27 = 100/3.

Answer: B
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Re: If 3^(6x) = 810,000, what is the value of (3^(x−1))^3?   [#permalink] 29 Nov 2017, 18:13
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