Question

8) Solve 4^(x - 2)= 8^6 A)5 B)8 C)10 D)11

Answer 1

Answer: OPTION D

Step-by-step explanation:

You need to remember the following:

$a^x=a^y\\x=y$

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

$4=2*2=2^2\\8=2*2*2=2^3$

Rewriting the expression:

$2^{2(x-2)}=2^{3(6)}$

Now you get:

$2(x-2)=3(6)$

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

Therefore, you get the following result:

$2x-4=18\\2x=22\\x=11$

Answer 2

For this case we have the following equation:

$4 ^ {(x-2)} = 8 ^ 6$

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

$2 ^ {2 * (x-2)} = 2 ^ {3 * 6}$

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

$2 (x-2) = 3 * 6\\2 (x-2) = 18\\2x-4 = 18\\2x = 18 + 4\\2x = 22\\x = \frac {22} {2}\\x = 11$

Answer:

$x = 11$

Option D