# Thread: write to single log

1. ## write to single log

How do I start this? to make it one log?

2. $\displaystyle Log(a/b) = log(a) - log(b)$
$\displaystyle log(ab) = log(a) + log(b)$
$\displaystyle a log(b) = log(b^a)$

3. Originally Posted by rj2001
How do I start this? to make it one log?
The start:

$\displaystyle 12 \log_6 \sqrt{5x - 4} - \log_6 \left(\frac{6}{x} \right) + \log_6 6$

$\displaystyle = 12 \log_6 (5x - 4)^{1/2} - \log_6 \left(\frac{6}{x} \right) + \log_6 6$

$\displaystyle = \log_6 (5x - 4)^6 - \log_6 \left(\frac{6}{x} \right) + \log_6 6$

where the first term is got using one of the usual rules.

Now add and subtract logs of the same base using the usual rules. Simplify.

4. Hello, rj2001!

Write as one log: .$\displaystyle 12\log_6\sqrt{5x-4} - \log_6\left(\frac{6}{x}\right) + \log_6(6)$

$\displaystyle \log_6\left(\sqrt{5x-4}\right)^{12} - \bigg[\log_6(6) - \log_6(x)\bigg] + \log_6(6)$

.$\displaystyle = \;\log_6(5x-4)^6 - \log_6(6) + \log_6(x) + \log_6(6)$

. . $\displaystyle = \;\log_6(5x-4)^6 + \log_6(x)$

. . $\displaystyle = \;\log_6\bigg[x(5x-4)^6\bigg]$