y = log2(x)
y = log(x) / log(2)
x = 2^(-y)
all 3 equations will create the identical graph.
this is because:
the log conversion formula says that log2(x) = log(x) / log(2)
the basic definition of logs says that y = log2(x) if and only if 2^y = x
your equation is y = -log2(x)
the base conversion formula becomes y = -log(x) / log(2).
the basic definition of logs says that y = log2(x) if and only if 2^y = x.
but your equation is y = -log2(x)
multiply both sides of this equation by -1 and you get:
-y = log2(x)
now use the basic definition to get -y = log2(x) if and only if 2^(-y) = x
this is the same as x = 2^-y which was graphed.
the alternative way to derive this is a little more convoluted but gets you the same equivalence.
start with y = -log2(x)
by the rules of logs, this is equivalent to y = -1 * log2(x) which is the same as y = log2(x^-1)
by the basic definition of logs, this is true if and only if 2^y = x^-1
since x^-1 is the same as 1/x, this becomes 2^y = 1/x
since 2^y is the same as 1/(2^-y), this becomes 1/(2^-y) = 1/x
this is true if and only if 2^-y = x which is the same as x = 2^-y
the graph is shown below:
