Respuesta :

alinakincsem

Answer:

x = -8

Step-by-step explanation:

We are given the following expression which we are to solve for [tex]x[/tex]:

[tex] 2 7 ^ x = 9 ^ { x - 4 } [/tex]

For this expression, we will make the bases same on both sides of the equation and then equate the exponents equal to each other.

[tex](3^3)^x = (3^2)^{x-4}[/tex]

Multiplying the exponents and equating them to get:

[tex] 3 x = 2 ( x - 4 ) [/tex]

[tex] 3 x = 2 x - 8 [/tex]

[tex] 3 x - 2 x = - 8 [/tex]

x = -8

carlosego

For this case we must solve the following equation:

[tex]27 ^ x = 9 ^ {x-4}[/tex]

We rewrite:

[tex]27 = 3 * 3 * 3 = 3 ^ 3\\9 = 3 * 3 = 3 ^ 2[/tex]

So:

[tex]3^{3(x)}=3^{2(x-4)}[/tex]

Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:

[tex]3 (x) = 2 (x-4)\\3x = 2x-8[/tex]

Subtracting 2x on both sides:

[tex]3x-2x = -8\\x = -8[/tex]

Answer:

[tex]x = -8[/tex]

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