Condense the logarithm

12. Log 10 - Log 5

13. Log x - Log 9

Question

Condense the logarithm 

12. Log 10 - Log 5


13. Log x - Log 9

zepdrix · Answer

$$\large\rm \log(a)-\log(b)=\log\left(\frac{a}{b}\right)$$

anonymous · Answer

so is the first one log10/ log 5= .301?

zepdrix · Answer

$\rm log(2)\approx 0.301$
yes :)

anonymous · Answer

Thanks! How do i do the second one?

anonymous · Answer

Since there is an x

zepdrix · Answer

For the first one, notice that we could have stopped here,$$\large\rm \log(10)-\log(5)\quad=\log\left(\frac{10}{5}\right)\quad=\log(2)$$So for the other question, that's where you'll stop after applying the rule.
No calculator step.

anonymous · Answer

so log x/ log  9 = log (9)? idk

zepdrix · Answer

Oh sorry :) I guess we're stopping even one step earlier than I realized,$$\large\rm \log(x)-\log(9)\quad=\log\left(\frac{x}{9}\right) \qquad\qquad \color{green}{\checkmark}$$Notice that when we use this rule, `we don't divide logs`.
We instead `divide the insides`.

You should not end up with two logs! :)

anonymous · Answer

ohhh okay (: can you help me with two more questions!! your my only hope because i have to leave soon and none else can help me with this