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?

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?

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

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?

Ultimate ENGAA Collection (with over 400 questions and solutions) book pdf from 2018

See https://www.chilimath.com/lessons/advanced-algebra/logarithm-rules/
The change base formula
Would it help?

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