# how to solve this logathrithm problem?

https://postimg.cc/7JVx6q24

not really sure on how to get the correct answer to this which is D.

at first I tried solving n^10 = n + 1 to get n = 1 but that was wrong.

I Dont understand the working for the given markscheme either. completely confused, any ideas?
Original post by MonoAno555
https://postimg.cc/7JVx6q24

not really sure on how to get the correct answer to this which is D.

at first I tried solving n^10 = n + 1 to get n = 1 but that was wrong.

I Dont understand the working for the given markscheme either. completely confused, any ideas?

The change base formula
Would it help?
Original post by MonoAno555
https://postimg.cc/7JVx6q24

not really sure on how to get the correct answer to this which is D.

at first I tried solving n^10 = n + 1 to get n = 1 but that was wrong.

I Dont understand the working for the given markscheme either. completely confused, any ideas?

Hi, I have the answer if you want. Are you still having problems?
Original post by Hehgxhrhfh
Hi, I have the answer if you want. Are you still having problems?

Please be aware of the forum rules which state that you should not provide solutions - only hints!

Original post by davros
Please be aware of the forum rules which state that you should not provide solutions - only hints!
Original post by MonoAno555
https://postimg.cc/7JVx6q24

not really sure on how to get the correct answer to this which is D.

at first I tried solving n^10 = n + 1 to get n = 1 but that was wrong.

I Dont understand the working for the given markscheme either. completely confused, any ideas?

could you also tell me where you got the problem from?
Original post by Hehgxhrhfh
could you also tell me where you got the problem from?

Ultimate ENGAA Collection (with over 400 questions and solutions) book pdf from 2018
Original post by MonoAno555
Ultimate ENGAA Collection (with over 400 questions and solutions) book pdf from 2018

Dont know how the model solution did it, but I presume it was using the change of base formula and cancelling/telescoping mentioned in #2? If so, a related way (if you forget the change of base formula) is to note its a product of logs so use the power rule
k*log(x) = log(x^k)
so for the first two you have
log_2(3)*log_3(4) = log_2(3^log_3(4)) = log_2(4)
with an obvious generalisation to the product of n-1 logs. As the power rule is used to derive the change of base formula, its a similar method.
(edited 9 months ago)
Original post by BankaiGintoki

Ty for this, I forgot this method
Original post by mqb2766
Dont know how the model solution did it, but I presume it was using the change of base formula and cancelling/telescoping mentioned in #2? If so, a related way (if you forget the change of base formula) is to note its a product of logs so use the power rule
k*log(x) = log(x^k)
so for the first two you have
log_2(3)*log_3(4) = log_2(3^log_3(4)) = log_2(4)
with an obvious generalisation to the product of n-1 logs. As the power rule is used to derive the change of base formula, its a similar method.

I got the answer actually with the change in base method. I was also not aware you could simply logs this way. Thanks
(edited 9 months ago)
Original post by MonoAno555
I got the answer actually with the change in base method. I was also not aware you could simply logs this way. Thanks

Its one way to prove the change of base formula as
log_a(b) = log_a(c^log_c(b)) = log_c(b) log_a(c)
so
log_c(b) = log_a(b) / log_a(c)