SOLUTION: graph y=-log2(x) with showing order pair solution

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Question 1081007: graph y=-log2(x)
with showing order pair solution
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
using the desmos.com calculator, you can graph this equation as follows:

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: