Write As Single Log

**magentarita** · November 13th 2008, 06:42 AM

Use the properties of logs to rewrite each expression as a single log. (log_b K - log_b M)- log_b a

MY WORK:

(log_b K - log_b M)- log_b a

Write as a single log.

I applied the rule log_(M/N) = log_b M - log_b N twice.

log_b(K/M) - log_b a....I could not stop here, right?

log_b[(K - a)/(M - a)]

Is this right? If not, why not?

**masters** · November 13th 2008, 12:01 PM

Originally Posted by magentarita

Use the properties of logs to rewrite each expression as a single log. (log_b K - log_b M)- log_b a

MY WORK:

(log_b K - log_b M)- log_b a

Write as a single log.

I applied the rule log_(M/N) = log_b M - log_b N twice.

log_b(K/M) - log_b a....I could not stop here, right?

log_b[(K - a)/(M - a)]

Is this right? If not, why not?

Here's what I did.

$\log_bK-\log_bM-\log_ba \Rightarrow \log_b\frac{K}{M}-\log_ba\Rightarrow\log_b\frac{\frac{K}{M}}{a}\Righ tarrow\boxed{\log_b\frac{K}{Ma}}$

I checked it with K=100, M=1000, a=10000 and using common log base 10.

$\log_bK-\log_bM-\log_ba \Rightarrow\log_{10}100-\log_{10}1000-\log_{10}10000={\color{red}-5}$

$\log_b\frac{K}{Ma}\Rightarrow\log_{10}\frac{100}{1 000\cdot 10000}={\color{red}-5}$

**magentarita** · November 13th 2008, 05:45 PM

Originally Posted by masters

Here's what I did.

$\log_bK-\log_bM-\log_ba \Rightarrow \log_b\frac{K}{M}-\log_ba\Rightarrow\log_b\frac{\frac{K}{M}}{a}\Righ tarrow\boxed{\log_b\frac{K}{Ma}}$

I checked it with K=100, M=1000, a=10000 and using common log base 10.

$\log_bK-\log_bM-\log_ba \Rightarrow\log_{10}100-\log_{10}1000-\log_{10}10000={\color{red}-5}$

$\log_b\frac{K}{Ma}\Rightarrow\log_{10}\frac{100}{1 000\cdot 10000}={\color{red}-5}$

Thank you for breaking it down just a bit more.

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