# Log Simplification?

• Apr 8th 2013, 02:01 AM
Quixotic
Log Simplification?
I am stuck on something that shouldn't be particularly complicated.

I have logx(xlogyy5)

Should I get 1+logx5? This doesn't look right to me.

Instructions much appreciated.
• Apr 8th 2013, 02:14 AM
ibdutt
Re: Log Simplification?
I think your approach is right. In case you find a discrepancy you may paste the same.
• Apr 8th 2013, 04:34 AM
topsquark
Re: Log Simplification?
Quote:

Originally Posted by Quixotic
I am stuck on something that shouldn't be particularly complicated.

I have logx(xlogyy5)

Should I get 1+logx5? This doesn't look right to me.

Instructions much appreciated.

It's correct. (Clapping)

-Dan
• Apr 8th 2013, 08:42 AM
Soroban
Re: Log Simplification?
Hello, Quixotic!

Quote:

$\text{I have: }\:\log_x(x\log_yy^5)$

$\text{Should I get: }\:1+\log_x5\,?$ . Yes!

$\log_5(x\log_yy^5) \;=\;\log_5(x\cdot 5\log_yy) \qquad\quad \text{Note that: }\log_yy =1$

. . . . . . . . . . $=\;\log_5(x\cdot 5\cdot 1)$

. . . . . . . . . . $=\;\log_5(5x)$

. . . . . . . . . . $=\;\log_55 + \log_5x \qquad\quad\text{Note that: }\log_55 = 1$

. . . . . . . . . . $=\; 1 + \log_5x$
• Apr 8th 2013, 12:59 PM
Quixotic
Re: Log Simplification?
Thanks everyone!