Thread: High school math analysis problem (log A)/A = C, solve for A

That is, if I'm going about it right. Trying to help my kid with math and totally stumped. Original problem is like this:

f(x) = 0.5^x
A * f(x) = f(x + A)
Solve for A.

I played around for a while and kept coming back to

(log A) / A = log 0.5

But I don't know where to go from there. The answer is given, but I couldn't figure out how to get there. Help!

That’s the best you can do if you’re using only logarithms. There is no way to write explicitly as a combination of elementary functions of .

However you can try the Lambert W function: this is not strictly speaking a function but a multivalued relation defined as iff .

.

If they allow it, you could also plot the two curves and find at what value of A they intersect:

solve ln(x)/x = ln(0.5) - Wolfram|Alpha