solve log2x-6^256=4

did you mean

log(2x-6)^256=4 ??

according to the numbers, I will assume so.
You must know your rules of logs

by definition
256 log (2x-6) = 4
log (2x-6) = 1/64
2x-6 = 10^(1/64)
2x-6 = 1.0366329..
2x = 7.0366...
x = 3.518316...

round to whatever accuracy you want.

that answer works on my calculator for my interpretation.
Let me know if you meant otherwise, brackets are critical .

To solve the equation log2x - 6^256 = 4, we need to isolate the variable x.

Step 1: Move the constant term to the other side of the equation.
log2x = 4 + 6^256

Step 2: Convert the logarithmic equation to an exponential equation.
2^(log2x) = 2^(4 + 6^256)

Step 3: Simplify the exponential equation.
x = 2^(4 + 6^256)

Step 4: Evaluate the exponent and calculate the value of x.
Use a calculator or programming code to compute 6^256, then add 4 to the result. Finally, raise 2 to that value to find the value of x.