Question

What would 7 log3 k + 6 log3 m – 9 log3 n be simplified? please explain

Answer 1

Let's first apply this rule of logs,\[\large a\cdot \log (b)=\log(b^a)\]Ok so the first term becomes,\[\huge7\cdot \log_3 k \qquad \rightarrow \qquad \log_3{k^7}\]Understand how that works? Think you can figure out the other 2 terms? :D

Answer 2

\[\log_{3} (m)^-9\]

Answer 3

sometin like that, i dont know how to properly use this

Answer 4

Ummm let's leave the negative on the outside, I think it will be a little easier to work with if we do that :)\[\large -9\log_3m \qquad \rightarrow \qquad -(9)\log_3m \qquad \rightarrow \qquad -\log_3m^9\]But yes you have the right idea :)

Answer 5

whats the next step?

Answer 6

\[\large \log(b)+\log(c)=\log(bc)\]\[\large \log(c)-\log(d)=\log(cd)\]We'll have to apply these rules to the problem. Here is how the first 2 would combine,\[\large \log_3{k^7}+\log_3{m^6} \qquad \rightarrow \qquad \log_3{(k^7\cdot m^6)}\]

Answer 7

Woops, I messed up the subtraction rule :O lemme fix that a sec.

Answer 8

\[\large \log(c)-\log(d)=\log\left(\frac{c}{d}\right)\]

Answer 9

Which would it be?
4 log3

4 log3 (k + m – n)

log3

log3

Answer 10

@zepdrix

Answer 11

I don't understand the options u pasted :( 3 of them are empty logs.. did they not paste correctly?

Answer 12

hold on

Answer 13

\[\frac{ km }{ n } \rightarrow \frac{ k^7m^6 }{ n^9 }\rightarrow \frac{ 42km }{9m }\rightarrow (k+m-n)\]

Answer 14

those are the options

Answer 15

It's the second one :o

If you're still confused by why, maybe look back at the rules for logarithms. :D

Answer 16

ok, i will thanks!