Question

Question #f182a

Answer 1

`x` can be equal to any real number greater than `0`.

Explanation:

We can prove that the expressions are equal, if we start with `log_2(x)`, we can apply the logarithm rule which says:
`log_a(b)=log_x(b)/log_x(a)`, where `log_x` can be any logarithm you choose.

Let's pick `log_16`:
`log_2(x)=log_16(x)/log_16(2)`

Since `log_16(2)=1/4`, we can simplify:
`log_16(x)/log_16(2)=log_16(x)/(1/4)=log_16(x)*4/1=4log_16(x)`

So we have proven that `log_2(x)=4log_16(x)` where x is a real number greater than zero (because otherwise the `log` functions aren't defined).