how to calculate this logarithmic operation

Welcome to the forum.

Some simple math here. Your expression is:

10 log (2 * 10**(x/10))

That is

10 log(2) + 10 log (10**(x/10) = 10 log(2) + 10 * x / 10 * log(10)

So result is simply:

10 log(2) + x log(10) = 6.931472 + 2.3025851 x

Works for log or log10 as you want.

That's much simpler (and gives a slightly more accurate result because there are less rounding effects) than the brute force computation):

var x : Float = 15 // Set the value of x

func compute(_ x: Float) -> Float {
    let x1 = x / 10
    let lnx = x1 * log(10)

    let p = exp(lnx)  // 10 ** (x/10)   //  log is Neper log, not log10

    let r = 10 * log(p + p)
    return r
}
print(compute(x))
let r = 10*log(2) + x*log(10)
print(r)

And check you get exactly the same result…

If that answers your question, don't forget to close the thread by marking the correct answer. Otherwise explain what you don't understand.