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

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asked Feb 28, 2024 834 views

1 Answer

Sarp Kaya · Answer 1 · 2024-03-04T20:54:48+0000

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_ .

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 $-1$.$