[SOLVED] logs

**lsnyder** · February 23rd 2009, 11:41 AM

Does anyone understand these two problems:

Problem 1:

(hint:

)

Problem 2:

help please?

for 1, I got -2k

& for 2, I got 3

which were wrong

**Chris L T521** · February 23rd 2009, 11:54 AM

Originally Posted by lsnyder

Does anyone understand these two problems:

Problem 1:

(hint:

)

Incorporating the hint, this is equivalent to:

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

Problem 2:

help please?

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?

**lsnyder** · February 23rd 2009, 12:01 PM

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

**lsnyder** · February 23rd 2009, 12:05 PM

oh nevermind, i figured out the 1/10 in the 1st problem

but i still don't follow the second one

**Chris L T521** · February 23rd 2009, 12:10 PM

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?

& on problem 2,
i am very lost.
where did the 3 come from in between 5 and -5

I applied rules of exponents:

$a^{b-c}=a^ba^{-c}$

**lsnyder** · February 23rd 2009, 12:15 PM

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?

**lsnyder** · February 23rd 2009, 12:39 PM

nevermind i got problem 2

if any1 cares the answer was:

15625/7776

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