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# P2 log question watch

1. totally stumpted, can anyone help?

log_2_x+4log_x_2=5

the answer is 2 or 16 according to the book
2. (Original post by James K)
totally stumpted, can anyone help?

log_2_x+4log_x_2=5

the answer is 2 or 16 according to the book
log2x + 4logx2 = 5

=> log2x + 4/[log2x] = 5

Let y = log2x:

=> y + 4/y = 5

=> y2 - 5y + 4 = 0

=> (y - 1) (y - 4)

y = 1 or y = 4

=> log2x = 1

=> x = 2

OR: log2x = 4

=> x = 16
3. is log_2_x log base two of x.

Well there you have it ^
4. i never knew that rule of switching four to divide it by the log....is that in the p2 book for edexcel??
5. (Original post by Finn)
i never knew that rule of switching four to divide it by the log....is that in the p2 book for edexcel??
It is certainly in the C2 book.

It can be "derrived" from the change of base rule.

As: logax = lobbx/logba

If you change the base to x:

logax = lobxx/logxa

But: lobxx = 1 (as x1 = x)

so: logax = 1/logxa
6. ooooh yeh cool thanks
7. cheers, that question has been doing my head in all day.

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