Question

4^(x+1)-6^x=2*3^(2x+2)

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve the equation 4^(x+1) - 6^x = 2 * 3^(2x+2), we'll simplify and manipulate the equation to solve for x.

Let's start by manipulating the equation step by step:

4^(x+1) - 6^x = 2 * 3^(2x+2)

Rewriting 4 as 2^2:

(2^2)^(x+1) - 6^x = 2 * 3^(2x+2)

Applying the exponent rule, (a^b)^c = a^(b*c):

2^(2(x+1)) - 6^x = 2 * 3^(2x+2)

Simplifying the left side of the equation:

2^(2x+2) - 6^x = 2 * 3^(2x+2)

Now, let's rewrite 6 as 2 * 3:

2^(2x+2) - (2*3)^x = 2 * 3^(2x+2)

Expanding the exponent on the left side:

2^(2x) * 2^2 - (2^x * 3^x) = 2 * 3^(2x+2)

Simplifying further:

4 * 2^(2x) - 2^x * 3^x = 2 * 3^(2x+2)

Dividing both sides by 2 to simplify:

2 * 2^(2x) - 2^(x+1) * 3^x = 3^(2x+2)

Now, let's rewrite 2 as 2^1:

2^(1+2x) - 2^(x+1) * 3^x = 3^(2x+2)

Since the bases on both sides of the equation are the same, we can equate the exponents:

1 + 2x = x + 1 + 2x

Simplifying the equation:

2x - x - x = 1 - 1

x = 0

Therefore, the solution to the equation 4^(x+1) - 6^x = 2 * 3^(2x+2) is x = 0.