(i) Write down the value of $
log 36.$
(ii) Express $2 log_3 + log_3 11$ as a single logarithm to base $a$. - Edexcel - A-Level Maths Pure - Question 5 - 2006 - Paper 2
Question 5
(i) Write down the value of $
log 36.$
(ii) Express $2 log_3 + log_3 11$ as a single logarithm to base $a$.
Worked Solution & Example Answer:(i) Write down the value of $
log 36.$
(ii) Express $2 log_3 + log_3 11$ as a single logarithm to base $a$. - Edexcel - A-Level Maths Pure - Question 5 - 2006 - Paper 2
Step 1
(i) Write down the value of log 36.
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Answer
To find the value of log36, we can use the properties of logarithms. Since 36 can be expressed as 62 or 22imes32, we can use these representations to simplify:
log 36 &= log(6^2) \
&= 2 log 6 \
&= 2 log(2 imes 3) \
&= 2 (log 2 + log 3).
distinguished in this context, the base of the logarithm must also be specified. Typically, $log$ refers to logarithm base 10 unless stated otherwise. In this case, we can directly refer to the value of $log 36$ without needing further transformation. Therefore:
The answer is simply:
log 36 = 2
Step 2
(ii) Express 2 log_3 + log_3 11 as a single logarithm to base a.
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Answer
For part (ii), we start with the expression:
2log3+log311.
First, apply the power rule of logarithms to the first term:
2log3=log3(32)=log39.
Thus, we can combine the logarithmic terms:
log39+log311=log3(9imes11).
