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If 3 to the power of -3x + 6 equals 27 to the power of x + 4, then x equals __________.

User Lsavio
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Answer:

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If 3 to the power of -3x + 6 equals 27 to the power of x + 4, then x equals _-1_ .

Explanation:

Let's solve the equation:


\[3^(-3x + 6) = 27^(x + 4)\]

First, express 27 as a power of 3, since both sides of the equation should have the same base:


\[27 = 3^3\]

Now substitute this into the equation:


\[3^(-3x + 6) = (3^3)^(x + 4)\]

Use the property
\(a^(mn) = (a^m)^n\):


\[3^(-3x + 6) = 3^(3(x + 4))\]

Now, set the exponents equal to each other:


\[-3x + 6 = 3(x + 4)\]

Expand and solve for x:


\[-3x + 6 = 3x + 12\]

Combine like terms:


\[6 = 6x + 12\]

Subtract 12 from both sides:


\[-6 = 6x\]

Divide by 6:


\[x = -1\]

Therefore,
\(x\) equals \(-1\).

User Sarp Kaya
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