Question

(3/5) ^8x-5>(9/25) ^4x+3

Answer 1

(3/5)^(8x - 5) > (3/5)^(2(4x + 3))

Так как 0 < 3/5 < 1, то знак меняется

(3/5)^(8x - 5) > (3/5)^(8x + 6)

8x - 5 < 8x + 6

x ∈ R

Answer 2

To solve the inequality (3/5)^(8x-5) > (9/25)^(4x+3), we can start by taking the logarithm of both sides. Let's take the natural logarithm (ln) for simplicity:

ln((3/5)^(8x-5)) > ln((9/25)^(4x+3))

Using the properties of logarithms, we can simplify the inequality:

(8x - 5)ln(3/5) > (4x + 3)ln(9/25)

Now, let's expand the logarithms:

(8x - 5)(ln 3 - ln 5) > (4x + 3)(ln 9 - ln 25)

Distribute and simplify:

8x(ln 3 - ln 5) - 5(ln 3 - ln 5) > 4x(ln 9 - ln 25) + 3(ln 9 - ln 25)

8xln3 - 8xln5 - 5ln3 + 5ln5 > 4xln9 - 4xln25 + 3ln9 - 3ln25

Now, let's collect the terms with x on one side and the constant terms on the other side:

8xln3 - 4xln9 > 8xln5 + 4xln25 + 5ln3 - 5ln5 - 3ln9 + 3ln25

Factor out x:

x(8ln3 - 4ln9) > 8ln5 + 4ln25 + 5ln3 - 5ln5 - 3ln9 + 3ln25

Divide both sides by (8ln3 - 4ln9):

x > (8ln5 + 4ln25 + 5ln3 - 5ln5 - 3ln9 + 3ln25) / (8ln3 - 4ln9)

Now we have the solution for x in terms of logarithms. You can use a calculator to approximate the value of x if needed.