c3 past paper maths help?

I was looking at a a past paper question that said show that:

y=5^(x+1) can be expressed as x= 1 + ( ln(y) / ln5 )

I dont undestand why they have used the natural long instead of log base 10?

Its question 4i of the ocr c3 june 2006 paper...thanks

Reply 1

Chlorophile

20

Original post by charlotte30

I was looking at a a past paper question that said show that:

y=5^(x+1) can be expressed as x= 1 + ( ln(y) / ln5 )

I dont undestand why they have used the natural long instead of log base 10?

Its question 4i of the ocr c3 june 2006 paper...thanks

Natural log is more useful. For instance, it is a lot easier to integrate when you use natural logs (you will find this out when you do C4). It would work with log base 10 but ln is just generally more useful.

Reply 2

joostan

13

Original post by charlotte30

I was looking at a a past paper question that said show that:

y=5^(x+1) can be expressed as x= 1 + ( ln(y) / ln5 )

I dont undestand why they have used the natural long instead of log base 10?

Its question 4i of the ocr c3 june 2006 paper...thanks

This is the same thing really, any two logarithms can be converted between by multiplication with a single constant, dependent on the bases you are converting. All logarithms are variations of the same basic function.

Also I hope that's

x=\dfrac{\ln(y)}{\ln(5)}-1

.

Reply 3

davros

16

Original post by charlotte30

I was looking at a a past paper question that said show that:

y=5^(x+1) can be expressed as x= 1 + ( ln(y) / ln5 )

I dont undestand why they have used the natural long instead of log base 10?

Its question 4i of the ocr c3 june 2006 paper...thanks

You could use any base of logarithm to get a similar answer. All you need to do is to show that if you use the natural log then you get the relationship given :smile:

c3 past paper maths help?

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