Question

(5/3)^(3x-7)=(5/3)^(5-x)

Answer 1

Ответ: х=3

Объяснение: 3х-7=5-х

                        4х=12

                        х=3

Answer 2

To solve the equation (5/3)^(3x-7) = (5/3)^(5-x), we can use the property of exponentiation that states that if two exponential expressions with the same base are equal, then their exponents must also be equal.

In this case, we have:

(5/3)^(3x-7) = (5/3)^(5-x)

Since the bases are the same (5/3), we can equate the exponents:

3x - 7 = 5 - x

Now, let's solve this equation for x.

First, let's simplify it by moving all the x terms to one side and the constant terms to the other side:

3x + x = 5 + 7

4x = 12

Divide both sides of the equation by 4:

x = 12/4

x = 3

Therefore, the solution to the equation (5/3)^(3x-7) = (5/3)^(5-x) is x = 3.