# Exam Log Question

#### CaptainBlack

##### Well-known member
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

##### Well-known member
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 question

CB

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