Respuesta :

carlosego

For this case we have the following equation:

[tex]4 ^ {(x-2)} = 8 ^ 6[/tex]

We must create equivalent expressions in the equation, so that they have equal bases:

[tex]2 ^ {2 * (x-2)} = 2 ^ {3 * 6}[/tex]

If the bases are the same, then the two expressions are only equal if the exponents are equal:

[tex]2 (x-2) = 3 * 6\\2 (x-2) = 18\\2x-4 = 18\\2x = 18 + 4\\2x = 22\\x = \frac {22} {2}\\x = 11[/tex]

Answer:

[tex]x = 11[/tex]

Option D

luisejr77

Answer: OPTION D

Step-by-step explanation:

You need to remember the following:

[tex]a^x=a^y\\x=y[/tex]

 Then, you must descompose 4 and 8 into their prime factors:

[tex]4=2*2=2^2\\8=2*2*2=2^3[/tex]

Rewriting the expression:

[tex]2^{2(x-2)}=2^{3(6)}[/tex]

Now you get:

[tex]2(x-2)=3(6)[/tex]

Finally, you must solve for the variable "x".

Therefore, you get the following result:

[tex]2x-4=18\\2x=22\\x=11[/tex]

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