Question

.........16^(2х-3)=(√8)^(x+1)

Answer 1

Ответ:

Привет,вот решение, не забудь поставить 5 звёзд и спасибо!;)

Пошаговое объяснение:

Answer 2

To solve the equation 16^(2x-3) = (√8)^(x+1), we need to simplify the expressions and find the value of 'x' that makes both sides of the equation equal.

Let's start by simplifying each side of the equation:

1. Simplify the left-hand side (LHS): 16^(2x-3) = (2^4)^(2x-3) = 2^(4(2x-3)) = 2^(8x-12)

2. Simplify the right-hand side (RHS): (√8)^(x+1) = (8^(1/2))^(x+1) = 2^(3/2 * (x+1)) = 2^(3x/2 + 3/2)

Now, the equation becomes: 2^(8x-12) = 2^(3x/2 + 3/2)

Since the bases (2 in this case) are the same, the exponents must be equal. Therefore, we can equate the exponents:

8x - 12 = 3x/2 + 3/2

To get rid of the fraction, we can multiply the entire equation by 2:

2(8x - 12) = 2(3x/2 + 3/2)

16x - 24 = 3x + 3

Now, let's isolate 'x' on one side of the equation:

16x - 3x = 3 + 24

13x = 27

Finally, solve for 'x':

x = 27 / 13

This is the solution for the equation 16^(2x-3) = (√8)^(x+1).