# log problem..is that correct my answer??

• Jun 28th 2010, 08:29 AM
mastermin346
log problem..is that correct my answer??
Given $\displaystyle log_3{7}=1.771$ and $\displaystyle log _3{5}=1.465$.find

a)$\displaystyle log_9{35}$

this is my step:
$\displaystyle =log{_\sqrt{9}}35^\frac{1}{2}$

$\displaystyle =\frac{1}{2}log_3(5)(7)$

$\displaystyle =\frac{1}{2}log_3{5}+log_3{7}$

$\displaystyle =\frac{1}{2}(1.465)+(1.771)$

$\displaystyle =2.5035$
• Jun 28th 2010, 08:32 AM
Ackbeet
I do not think your answer is correct. I imagine you're supposed to use the properties of logarithms to combine the given information in such a way that you can compute the required logarithm. Note that the bases are different. What do you suppose you have to do there?
• Jun 28th 2010, 08:37 AM
mastermin346
what should i do?
• Jun 28th 2010, 08:45 AM
Ackbeet
Well, you're given $\displaystyle \log_{3}(7)$ and $\displaystyle \log_{3}(5)$. You're after the quantity $\displaystyle \log_{9}(35)$. What you'd like to do is have the bases multiply, and the arguments multiply. If you look at this page, does it give you any ideas on how to do that?
• Jun 28th 2010, 08:47 AM
earboth
Quote:

Originally Posted by mastermin346
Given $\displaystyle log_3{7}=1.771$ and $\displaystyle log _3{5}=1.465$.find

a)$\displaystyle log_9{35}$

this is my step:
$\displaystyle =log{_\sqrt{9}}35^\frac{1}{2}$

$\displaystyle =\frac{1}{2}log_3(5)(7)$

$\displaystyle =\frac{1}{2}log_3{5}+log_3{7}$

$\displaystyle =\frac{1}{2}(1.465)+(1.771)$

$\displaystyle =2.5035$

All your considerations and calculations are OK. There is only a pair of brackets missing:

$\displaystyle =\frac{1}{2}\left((1.465)+(1.771)\right)$
• Jun 28th 2010, 08:47 AM
Ackbeet
Hang on. Just saw something in the OP. Try re-computing the last number from the second-to-last line. That's an average. Your answer at the end is clearly wrong, but I think the steps up to that point are correct.

[EDIT] Earboth sees the problem correctly.