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A level Core 2 Log question watch

The graph of y=ax^n passes through the points (1,2) and (-2,32)
Find exact values of a and n
2. If passes through (1, 2), then you can substitute this in to find an equation. You can do the same for (-2, 32).
3. (Original post by Integer123)
If passes through (1, 2), then you can substitute this in to find an equation. You can do the same for (-2, 32).
a=2
n=4
???
4. (Original post by Greenapplepear)
a=2
n=4
???
Yeah that's correct
5. Yay, thank you so much!
(Original post by Integer123)
Yeah that's correct
6. jj
7. (Original post by Integer123)
Yeah that's correct
When you make the substitution you get:
32 = 2 (-2)^n
-2^n=16

I know n=4 is the correct answer but how do you take log of a negative number?
8. (Original post by Kartheyan)
When you make the substitution you get:
32 = 2 (-2)^n
-2^n=16

I know n=4 is the correct answer but how do you take log of a negative number?
You can't take the log of a negative number in this context. Basically, where , so it's best to ignore the log of a negative number.

Instead, only has real values when x is an integer, and is only positive when x is an even integer. By inspection, we then get n=4.

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