Question

(3/2)^1-2x=(8/27)^x+3

Answer 1

Если правильно поняла условие, то вот

Answer 2

To solve the equation (3/2)^(1-2x) = (8/27)^(x+3), we can start by expressing both sides of the equation with the same base. In this case, we can choose to express both sides with a base of 3:

(3/2)^(1-2x) = (8/27)^(x+3)

Rewriting the bases:

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

Now, simplify the right side:

(3/2)^(1-2x) = (3^(2x+6))/(3^(3x+9))

Since the bases are the same, we can equate the exponents:

1 - 2x = 2x + 6 - (3x + 9)

Simplifying the right side:

1 - 2x = 2x + 6 - 3x - 9

Combining like terms:

1 - 2x = -x - 3

Now, let's isolate the variable x. Add 2x to both sides and add 3 to both sides:

1 + 3 = -x + 2x - 3x

4 = -2x

Divide both sides by -2:

4 / -2 = x

x = -2

Therefore, the solution to the equation is x = -2.