Solution:

We are given the equation (4/11)^(x-1) = (11/4)^(2x-5)

Step 1:
Let's simplify both sides of the equation by taking the logarithm.

Taking the logarithm of both sides of the equation, we get:

log((4/11)^(x-1)) = log((11/4)^(2x-5))

Using the logarithmic rule log a^b = b*log a, we can simplify the equation as:

(x-1)log(4/11) = (2x-5)log(11/4)

Step 2:
Let's solve for x.

Simplifying the equation further, we get:

xlog(4/11) - log(4/11) = 2xlog(11/4) - 5log(11/4)

Rearranging, we get:

xlog(4/11) - 2xlog(11/4) = 5log(11/4) - log(4/11)

Factoring out x, we get:

x(log(4/11) - 2log(11/4)) = 5log(11/4) - log(4/11)

Simplifying, we get:

x = (5log(11/4) - log(4/11)) / (log(4/11) - 2log(11/4))

Step 3:
Let's solve for x using a calculator.

Using a calculator, we get:

x ≈ 1.4

Therefore, x is approximately 1.4.

Conclusion:

Hence, the value of x in the given equation is approximately 1.4.