Higher Prelim Exam: Solving Log Questions

[CaptainBlack]

A Question from Em on Yahoo answers:

Please can someone help with this question from a Higher Prelim paper? [A knowledge of how to change log bases is not a requirement of the syllabus.]7(a) Given that log_4(x)=P, show that log_16(x) =1/2P
(b) Solve log_3(x)+log_9(x)=12

 

[CaptainBlack]

A Question from Em on Yahoo answers:

Please can someone help with this question from a Higher Prelim paper? [A knowledge of how to change log bases is not a requirement of the syllabus.]7(a) Given that log_4(x)=P, show that log_16(x) =1/2P
(b) Solve log_3(x)+log_9(x)=12

What you need to use is the definition of a logarithm: \( \log_a (b)=c \) means that \( a^c=b \).

The other thing you need to do these is to observe that:
\[ (a^2)^{c/2}=a^c=b \]
so:
\[\log_{a^2} (b)=c/2 =\frac{ \log_a (b)}{2}\]
Which is as far as I will go as this is an exam questionCB