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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?

See https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/
The change base formula
Would it help?
Reply 2
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?
Reply 3
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!
Reply 4
:yy:
Original post by davros
Please be aware of the forum rules which state that you should not provide solutions - only hints!
Reply 5
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?
Reply 6
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
Reply 7
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)
Reply 8
Original post by BankaiGintoki

Ty for this, I forgot this method
Reply 9
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)
Reply 10
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)

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