Question

8) Solve 4^(x - 2)= 8^6

A)5

B)8

C)10

D)11

Answer 1

Answer: OPTION D

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