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# Logarithms homework question. watch

1. Hi, a question has me trumped on my homework, it says to evaluate:

My working:

I believe I did work out the correct answer of 8, but I'm not sure solving the logarithm as an index of 2 is the correct way to go about it. Has anybody any advice on the proper way to go about solving this? Thanks.
2. The main problem is, of course, to evaluate log28 - once you've done that it's a simple matter to raise two to that power.

To compute log28, you want to find x such that 2x=8, and this appears to be what you've done even if your notation is somewhat weird. You should define what x is before introducing it to an equation, and you shouldn't "nest" equations like you've done.

A clearer and more correct way to write what you've done is the following:

let
then
and
which gives (alternatively you could simply spot that x=3 from line 2)
therefore

Overall, however, the simplest thing to do is to notice that log2 is the inverse function of raising 2 to a power, and hence
for any a.

In fact, in general,

for any a and any b
3. Could anybody help me with this question please? Any pointers?
Given that:

find the value of x.

I know I'm supposed to show that becomes , but I don't know where to go from there, any pointers? Thanks.
4. (Original post by Marcum)
Could anybody help me with this question please? Any pointers?
Given that:

find the value of x.

I know I'm supposed to show that becomes , but I don't know where to go from there, any pointers? Thanks.
log(x)+log(y)=log(xy)
5. (Original post by james22)
log(x)+log(y)=log(x)+log(y).
Don't you mean log(x)+log(y)=log(xy)?
6. (Original post by brianeverit)
Don't you mean log(x)+log(y)=log(xy)?
Lol yes it is, although what I wrote was technically true
7. You can also use
Log(x) - log(y) = log(x/y)

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8. Which is incidentally an equivalent rule!
Spoiler:
Show
log(x) - log(y) = log(x) + (-log(y)) = log(x) + log(1/y) = log(x*1/y) = log(x/y)
9. Sorry I was eating my tea. I got . Is that correct?
10. (Original post by Marcum)
Sorry I was eating my tea. I got . Is that correct?
yes
11. Yes

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Updated: January 22, 2014
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