Question

2*16^x-2^4x-4^2x-2=15

Answer 1

$2* 16^{x}- 2^{4x}- 4^{2x-2}=15 2* ( 2^{4} )^{x} - 2^{4x} - ( 2^{2} )^{2x-2} =15 2* 2^{4x} - 2^{4x} - 2^{4x-4} =15 2*2 ^{4x} -1* 2^{4x} - \frac{1}{ 2^{4} } * 2^{4x} =15 2^{4x}*(2-1- \frac{1}{16} ) =15$
$2^{4x}* \frac{15}{16} =15 |: \frac{15}{16} 2^{4x}=16 2^{4x} = 2^{4}$
4x=4

x=1

Answer 2

To solve the equation 2*16^x - 2^(4x) - 4^(2x) - 2 = 15, we need to find the value of x that satisfies the equation. The first step is to simplify the terms involving exponents.

1. Rewrite 16 as 2^4 (since 16 = 2^4).
2. Rewrite 4^2x as (2^2)^2x and then simplify it to 2^(22x) = 2^(4x) (using the property (a^b)^c = a^(bc)).
3. Rewrite 2^(4x) as (2^2)^2x and then simplify it to 4^(2x) (using the property a^(2b) = (a^b)^2).

Now the equation becomes:

2*(2^4)^x - 2^(4x) - 4^(2x) - 2 = 15.

Simplify further:

2*2^(4x) - 2^(4x) - 4^(2x) - 2 = 15.

Next, combine the terms with the same base:

2^(4x) - 4^(2x) - 2 = 15.

Now, let's focus on the terms with the same base:

1. 2^(4x) - 4^(2x)

As we established earlier, 4^(2x) is equal to 2^(4x). So, we can rewrite the equation as:

2^(4x) - 2^(4x) - 2 = 15.

Since the two terms cancel each other out, we get:

-2 = 15.

This is a contradiction, and there is no valid solution for x that satisfies the equation. Therefore, the original equation has no solution.