Tìm n biết: ( 1/3 + 1/6 ) . 2^n+4 -2^n = 2^14 - 2^10

To solve the equation, we can start by simplifying the left side:

(1/3 + 1/6) * 2^(n+4) - 2^n = 2^14 - 2^10

To simplify the left side, we need to find a common denominator for 1/3 and 1/6, which is 6. So we can rewrite the equation as:

(2/6 + 1/6) * 2^(n+4) - 2^n = 2^14 - 2^10

Now we can combine the fractions:

3/6 * 2^(n+4) - 2^n = 2^14 - 2^10

Simplifying further:

1/2 * 2^(n+4) - 2^n = 2^14 - 2^10

Now we can simplify the powers of 2:

2^(n+1) - 2^n = 2^14 - 2^10

To solve for n, we can subtract 2^n from both sides:

2^(n+1) - 2^n - 2^n = 2^14 - 2^10 - 2^n

Simplifying:

2^(n+1) - 2^n - 2^n = 2^14 - 2^n - 2^10

Now we can combine like terms:

2^(n+1) - 2^n - 2^n = 2^14 - 2^n - 2^10

2^(n+1) - 2^n - 2^n = 2^14 - 2^10 - 2^n

Next, we can simplify the left side:

2 * 2^n - 2^n - 2^n = 2^14 - 2^10 - 2^n

2^n - 2^n - 2^n = 2^14 - 2^10 - 2^n

Now we can combine like terms:

-2^n = 2^14 - 2^10 - 2^n

To isolate n, we can add 2^n to both sides:

-2^n + 2^n = 2^14 - 2^10 - 2^n + 2^n

Simplifying:

0 = 2^14 - 2^10

Since 2^14 is greater than 2^10, the equation is not possible. Therefore, there is no solution for n that satisfies the equation.