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How to get to final answer (mark scheme) - easy - C2!

How do you get from Step 2 to Step 3? I know it involves log rules, but I have the inequality arrow going the other way :frown:

Help!

Thanks.
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Original post by TheKevinFang
How do you get from Step 2 to Step 3? I know it involves log rules, but I have the inequality arrow going the other way :frown:

Help!

Thanks.


It may help to write 300/480 as 5/8. Then 1 - (0.75)^n > 5/8 and so 3/8 > (0.75)^n.

Taking the log of both sides, you get log(3/8) > nlog(0.75).

Now here's where the sign change comes in. Notice that, for something like 6 < 8, if we multiply or divide both sides by a negative number (to keep it simple choose -1) we get -6 > -8. Now, how is that relevant?

(Rather nasty for 1 mark).
Original post by SeanFM

Now here's where the sign change comes in. Notice that, for something like 6 < 8, if we multiply or divide both sides by a negative number (to keep it simple choose -1) we get -6 > -8. Now, how is that relevant?
.

I'm not sure to be honest with you, I just divided both sides by log (0.75), and got:

n < log(0.375)/log(0.75)?

It might be right in front of my eyes, but I'm still not sure about the sign change :frown:
Original post by TheKevinFang
I'm not sure to be honest with you, I just divided both sides by log (0.75), and got:

n < log(0.375)/log(0.75)?

It might be right in front of my eyes, but I'm still not sure about the sign change :frown:


It is just as you divide both sids by log(0.75) that the sign flips.

It may help to think about my previous hint, and now I'll tell you that log(1) is 0 and the log of anything between 0 and 1 is a negative number.. which includes log(0.75) and then think about my previous hint.

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