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If 8*3^7 = 3^x - 3^(x - 2), what is the value of x?

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If 8*3^7 = 3^x - 3^(x - 2), what is the value of x? [#permalink] New post   15 May 2022, 22:46
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If \(8*3^7 = 3^x - 3^{x-2}\), what is the value of x?

A. 1
B. 3
C. 7
D. 9
E. 12


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D
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If 8*3^7 = 3^x - 3^(x - 2), what is the value of x? [#permalink] New post   16 May 2022, 03:32
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\(8*3^7 = 3^x - 3^{x-2}\)

\(8 * 3^7 = 3^x - \frac{3^x}{9}\)

Multiplying both the sides with \(9\)

\(9 * 8 * 3^7 = 9 * 3^x - 3^x\)

\(3^{2+7} = 3^x\)

\(x = 9\)

Answer \(D\)
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Re: If 8*3^7 = 3^x - 3^(x - 2), what is the value of x? [#permalink] New post   16 May 2022, 06:18
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Carcass wrote:
If \(8*3^7 = 3^x - 3^{x-2}\), what is the value of x?

A. 1
B. 3
C. 7
D. 9
E. 12


Given: \((8)(3^7) = 3^x - 3^{x-2}\)

Factor the right side: \((8)(3^7) = 3^{x-2}(3^2 - 1)\)

Evaluate the part in brackets: \((8)(3^7) = 3^{x-2}(8)\)

Divide both sides of the equation by \(8\) to get: \(3^7 = 3^{x-2}\)

Since the bases are equal, we know that \(7 = x-2\), which means \(x = 9\)

Answer: D
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Re: If 8*3^7 = 3^x - 3^(x - 2), what is the value of x? [#permalink]
16 May 2022, 06:18
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