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Maths C2 Logs.

Im not sure whether I fully understand logs =/. Can anyone please go through these questions with me ?

The nth term of the geometric series is Un, and the (2n)nth term is U2n.
( r=3/4, a=48).
Write Un and u2n in terms of n.
Hence show log10(Un)-log10(U2n)=nlog10(4/3)

hence show the value of log10(u100/u200)= 12.5 to 3sf.

and:

(1+root5)^4= 56 + 24root5
hence show that log2(1+root5)^4=K+log2(7+3root5) where k is an integer.

Thanks. :woo:

Reply 1

hazzypants

I HATE LOGS!!!!! When i get home, I will try and send you a solution.

Reply 2

skatealexia

un = 48x3/4^n-1
u2n= 48x 3/4^2n-1?

Reply 3

skatealexia

48x3/4^n-1 / 48 x 3/4^2n-1 = 1x3/4^1/2 3/4 x 1/2 = 3/8 :s-smilie:

3/4^-n

= 4/3^n
?

I can

Hey I have understood it up to here, how do you do the next part of the question?

Reply 7

Jessicaaaa11

How do you show that log10(un)-log10(u2n) = nlog10(4/3) ?

Reply 8

aoxa

Original post by Jessicaaaa11

How do you show that log10(un)-log10(u2n) = nlog10(4/3) ?

You know what Un and u2n are - If you're not sure check out unbounded's post.

Then use the log law log(x) - log(a) = log(x/a) as long as the base (here it's to the base 10) is the same.