# Logarithm question

• Oct 1st 2011, 08:59 AM
David Green
Logarithm question
I have a log question which asks me to express the log of a single number?

The examples I have seen are in both decimal answers and fractions, I am wondering what way the answer to a log question should be given?
• Oct 1st 2011, 09:30 AM
Quacky
Re: Logarithm question
It depends on the question, really. Generally, I'd go with fractions because they tend to be easier to look at/work with, particularly with logs, and they give you an exact result whereas decimals can't always do that.
• Oct 1st 2011, 09:40 AM
e^(i*pi)
Re: Logarithm question
Quote:

Originally Posted by David Green
I have a log question which asks me to express the log of a single number?

The examples I have seen are in both decimal answers and fractions, I am wondering what way the answer to a log question should be given?

Whatever the question wants. Like Quacky I prefer fractions since they are easier to manipulate using the log laws - especially $\log_c \left(\dfrac{a}{b}\right) = \log_c(a) - \log_c(b)$
• Oct 1st 2011, 10:08 AM
David Green
Re: Logarithm question
I have worked out the answer which is 3.10 or log9 30 / log9 3, the questions says the result should be a number, so I assume that 3.10 is the answer, but am not sure whether I should answer it as 3 or 3.10?
• Oct 1st 2011, 10:15 AM
e^(i*pi)
Re: Logarithm question
Quote:

Originally Posted by David Green
I have worked out the answer which is 3.10 or log9 30 / log9 3, the questions says the result should be a number, so I assume that 3.10 is the answer, but am not sure whether I should answer it as 3 or 3.10?

$\dfrac{\log_9(30)}{\log_9(3)} = \dfrac{\log_9(10)+\log_9(3)}{\log_9(3)} = \dfrac{\log_9(10)}{\log_9(3)} + 1$

Since $3 = 9^{1/2} \text{ then } \log_9{3} = \log_9(9^{1/2}) = \dfrac{1}{2}$ we can put this into our equation above:

$\dfrac{\log_9(10)}{\log_9(3)} + 1 = 2\log_9(10) + 1$

edit: this is approximately equal to 3.1 but it is better to leave it in exact form to avoid rounding errors. If this were my question I'd leave it in the form above: $2\log_9(10) +1$
• Oct 1st 2011, 12:35 PM
Quacky
Re: Logarithm question
Quote:

Originally Posted by e^(i*pi)
If this were my question I'd leave it in the form above: $2\log_9(10) +1$

This is ideal, however the OP should check with their teacher. I remember in one of my previous modules, anything with logs in the final answer was not deemed "fully simplified" - the mark scheme would specify that either a decimal or a fractional equivalent were acceptable. And I won't even talk about the mechanics...
• Oct 1st 2011, 02:07 PM
David Green
Re: Logarithm question
Quote:

Originally Posted by Quacky
This is ideal, however the OP should check with their teacher. I remember in one of my previous modules, anything with logs in the final answer was not deemed "fully simplified" - the mark scheme would specify that either a decimal or a fractional equivalent were acceptable. And I won't even talk about the mechanics...

I believe the methods shown have given me a more in depth understanding of the log system although I had already previously worked out the solution myself, the members of this forum that have given clarification for me I would like to say thank you for your support.

I have contacted my tutor for clarification with regards how to present the answer, so will have to wait until I get a response, which I know will be soon, so I will advise of what I am told later.