Hello, bobak!

Here's the first one . . .

Given: .

calculate to three decimal places.

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- February 28th 2008, 11:54 AM #1

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## Log Question

To nine decimal places, and

i) Calculate and to three decimal places. By taking logs, or otherwise, show that

Hence write down the first digit of

ii) Find the first digit of each of the following numbers: , and

[OCR STEP I 2000, Question 1]

- Bobak

- February 28th 2008, 12:52 PM #2

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- February 28th 2008, 01:54 PM #3

- February 28th 2008, 02:04 PM #4
For the final bit, try to apply the reasoning from earlier:

Can it be shown that , where obviously a and x aren't known yet!

Note that . So clearly x = 301.

So can you find an a such that . In other words, can you find an a such that

.

Again, you'd use the known values of log from earlier. Warning: spoiler below.

Answer: a = 1 so the first digit is 1.

- February 28th 2008, 02:09 PM #5

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- February 28th 2008, 02:12 PM #6

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