[SOLVED] logs

• Feb 23rd 2009, 11:41 AM
lsnyder
[SOLVED] logs
Does anyone understand these two problems:

Problem 1:
https://webwork.uncc.edu/webwork2_fi...36fe4c71e1.png (hint: https://webwork.uncc.edu/webwork2_fi...29a8a6dbf1.png )

Problem 2:
https://webwork.uncc.edu/webwork2_fi...f72c808921.png

for 1, I got -2k

& for 2, I got 3

which were wrong
• Feb 23rd 2009, 11:54 AM
Chris L T521
Quote:

Originally Posted by lsnyder

Incorporating the hint, this is equivalent to:

$\log_{1048576}\left[\left(\left[1048576^{\frac{1}{10}}\right]^{-2}\right)^k\right]=\log_{1048576}\left[\left(1048576\right)^{-\frac{2k}{10}}\right]$ $=-\frac{k}{5}\log_{1048576}\left(1048576\right)=\col or{red}\boxed{-\frac{k}{5}}$

Quote:

Problem 2:
https://webwork.uncc.edu/webwork2_fi...f72c808921.png

for 1, I got -2k

& for 2, I got 3

which were wrong
Note that $3^{6\log_3 5-5\log_3 6}=3^{6\log_3 5}3^{-5\log_3 6}=3^{\log_3\left(5^6\right)}3^{\log_3\left(6^{-5}\right)}$

Can you finish the simplification?

Does this make sense?
• Feb 23rd 2009, 12:01 PM
lsnyder
okay i somewhat ubderstand 1.
i just don't understand where u got 1/10.
other than that i get it.

& on problem 2,
i am very lost.
where did the 3 come from in between 5 and -5
• Feb 23rd 2009, 12:05 PM
lsnyder
oh nevermind, i figured out the 1/10 in the 1st problem

but i still don't follow the second one
• Feb 23rd 2009, 12:10 PM
Chris L T521
Quote:

Originally Posted by lsnyder
okay i somewhat ubderstand 1.
i just don't understand where u got 1/10.
other than that i get it.

In the hint, $1048576=4^{10}\implies 1048576^{\frac{1}{10}}=4$. Thus, in your expression, I substituted $1048576^{\frac{1}{10}}$ for $4$.

Does this clarify things?

Quote:

& on problem 2,
i am very lost.
where did the 3 come from in between 5 and -5
I applied rules of exponents:

$a^{b-c}=a^ba^{-c}$
• Feb 23rd 2009, 12:15 PM
lsnyder
yea i got the 1/10 after i posted i didn't understand.
but problem 1 i understand.

now on problem 2,
i see what you did with the 3.
i have 1 question though.
Will all the threes cancel out?
or is there something else i am missing?
• Feb 23rd 2009, 12:39 PM
lsnyder
nevermind i got problem 2

if any1 cares the answer was:

15625/7776