00:01
In the given question we are told to use some technology to find points and then graph the function of y equal to minus 2, y equal to minus 2 times log with base 2 of minus x plus 5 plus 1.
00:23
So what we are told to do is to graph this uh graph this function and plot at least 4.
00:31
Four points so what we could do over here is we can take this table that is x y and in this table we have to upload at least four points with integer coordinates is what we are being told so let's write when we take the graph of this graph of this graph of this graph of of this function what we could see is that we can start by substituting some values of x into this function in order to find the values of y and we are specifically told to plode points which have integer coordinates right so what this means is that we cannot take points which has coordinates which have decimals or fractions we should take integers so, we have a property that log with base 2 of log with base a of a to the power b is equal to the power of a which is b itself.
01:48
So this is a property that we can, a logarithmic property that we can use.
01:53
That is when we take the log with base a of a to the power b, we get the result as b itself.
02:00
So over here when we take log with base 2 of 2 to the power 1 it should be equal to 1 similarly if it is log with base 2 raised to 2 to the power 2 it would be equal to 2 when it is 2 to the power of 3 it would be equal to 3 and when it is log with base 2 to the power of 4 it would be equal to 4 so this is exactly that we are what we are going to do over here what we are going to do is first we are going to make minus x plus 5 equal to 1 right so first point would be x equal to 4 so minus 4 plus 5 is equal to 5 is equal to point is going to be 3.
03:00
So minus 3 plus 5 is going to be 2 which means log with base 2 of 2 is equal to 1 minus 2 plus 1 is equal to minus 1.
03:14
So that is one point that we can mark on the graph which would have integer coordinates that is minus 3 comma minus 1 right so this is one point that we can mark on this graph and moving on with the next part when we take 5 when we take x equal to 3 1 we get this term as minus minus plus 5 which is 4 so log 2 square is 4 so we will have minus 2 times 2 which would be minus 4 plus 1 which is minus 3 moving on to the next one we can take 2 cube is 8 so for minus x plus 5 to be equal to 8 what we would have to do is we would have to take the value of of x as 5 minus x is equal to 8.
04:41
X should be equal to 5 minus 8 which is minus 3.
04:44
So when x equal to minus 3, then log with base 2 of minus x plus 5 would become, would have a value of 3.
04:55
Minus 2 times 3 is minus 6 and minus 6 plus 1 is minus 5...