How do I do this logarithm by hand. log2(log3(y))=3?

Question

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i have some questions on how to solve this. thnx

Answer 1

log2(log3(y))=3
log3(y) = 2^3
log3(y) = 8
y = 3^8
y = 6561

Answer 2

It's unclear what you mean by "solve a logarithm", since you solve equations, and you don't mention what kind of equation you might mean that involves logarithms If you mean "compute a logarithm by hand" then, depending on what base you're working in, some logarithms can be exactly computed by hand (e.g. in base 10 logs, log(100) is exactly 2). But in general, most numbers are not whole powers or even rational powers of the base, and in that sense if you want a numerical answer you have to stop at some decimal approximation - but these decimal approximations can certainly be computed by hand. I've done it myself many times. Calculators probably use a series expansion. When doing problems by hand, there are other approaches, depending on the problem; you mightbe able to make use of Newton's method in some cases for example

Answer 3

log2(log3(y))=3

since (LOGa(b) = c) == (a^c = b)

2^3 = log3(y)
3^(2^3) = y

3^(8) = y

6561=y

Answer 4

DUde, you asked this question 20 min before and we have already answered it

Answer 5

log[base2](log[base3](y)) = 3
2^{log[base2](log[base3](y))} = 2^3
log[base3](y) = 2^3 = 8
3^{log[base3](y)} = 3^8
y = 3^8 = 6561