VCE Methods Question Thread!

[kinslayer]

Yeah, doesn't matter, just whichever base you can calculate. Though the base e logarithm is definitely more common in mathematics

[knightrider]

How would you do this question?

Solve for x given that ?

[keltingmeith]

When you use the change of base rule how do you decide what base to make both the numbers?

You change to one that's useful, but normally you'll be told what base to change to.

How would you do this question?

Solve for x given that ?

So, let y=log_4(p):

[knightrider]

You change to one that's useful, but normally you'll be told what base to change to.



So, let y=log_4(p):

Thanks eulerfan101 

but my book says the answer is     
How did they get this?

[keltingmeith]

Thanks eulerfan101 

but my book says the answer is     
How did they get this?

Change of base rule.

[Floatzel98]

Change of base rule.

Would they have used change of base rule from the start or would they have used the same method as you then just change of base at the end? Is one accepted as a simpler form over the other?

[keltingmeith]

Would they have used change of base rule from the start or would they have used the same method as you then just change of base at the end? Is one accepted as a simpler form over the other?

Both methods of doing it are acceptable and perfectly fine, you'll get the same answer at the end. Neither is objectively "simpler" than the other, and both have pros or cons. Write it in the way that you're less likely to make a mistake with.

[knightrider]

Why doesn't my way of working out work for the question attached?

[Stevensmay]

Why doesn't my way of working out work for the question attached?

You've gone from
to 2x-b-1=5, this isn't valid.

[knightrider]

You've gone from
to 2x-b-1=5, this isn't valid.

Thanks Stevensmay



EDIT:just realised all the bases have to be the same to equate and the 5 isnt isnt the same base as 4 

[knightrider]

For this question attached they used in the answer but you could use any base log right?

[cosine]

For this question attached they used in the answer but you could use any base log right?

Yes you can use any base of a log, as long as you use the same base on both sides as you take the log of both sides, the answers will still be valid!

[kinslayer]

For this question attached they used in the answer but you could use any base log right?

Can use log to any base, but if you have a calculator that does natively then I would use that. Saves a couple button pushes because that way you only have to work out and not and

[cosine]

f(x) =

Find the largest domain (positive) that will satisfy the inverse function, so that it becomes a 1:1 function. This is a circle, of equation:



So the domain = [-4, 4], range = [-4, 4]
But for the function to be a 1:1 in order to satisfy the inverse function, the domain is restricted to: [0, 4], meaning the range is: [-4, 4]

So that means the domain of the inverse must equal the range of the 1:1 function, which is [-4,4]

The answer is not this however, can someone help? Cheers

[wunderkind52]

f(x) =

Find the largest domain (positive) that will satisfy the inverse function, so that it becomes a 1:1 function. This is a circle, of equation:



So the domain = [-4, 4], range = [-4, 4]
But for the function to be a 1:1 in order to satisfy the inverse function, the domain is restricted to: [0, 4], meaning the range is: [-4, 4]

So that means the domain of the inverse must equal the range of the 1:1 function, which is [-4,4]

The answer is not this however, can someone help? Cheers

Are you applying a restriction to f(x)? In that case, take note that it is the top semicircle, so in that case the range is [0,4]