Question

logbase3(x)+logbase3(x+6)=3

Answer 1

\[\log_3(x)+\log_3(x+6)=\log_3(x(x+6))\] is a start

Answer 2

\[\log_{3} (x^2+6x)=3\]

then i get lost

Answer 3

rewrite in equivalent exponential form
\[\log_b(x)=y\iff b^y=x\]

Answer 4

you should be able to switch back and forth easily
will make life much easier
math life anyways

Answer 5

if i do \[\log_{3} 3 \]

then that equals one, and x^2+6x=1 I can't factor if I bring it to the other side, the 3 becomes a 27 somehow. What property is it called

Answer 6

\[\log_7(49)=2\iff 7^2=49\] etc

Answer 7

it is the meaning of the log

Answer 8

\[10^3=1000\iff \log_{10}(1000)=3\]

Answer 9

Oh I see... but logbase3(3) = 1

Answer 10

the teacher got 27 somehow, as 3^1 = 3

Answer 11

lets go slow
you are not "taking the log" of both sides

Answer 12

Ok, thank you for your patience first of all.... I am combining logs using a property on the left side

Answer 13

how would you solve
\[\log_2(x)=3\] for \(x\) ?

Answer 14

2^3

Answer 15

got it

Answer 16

how would you solve
\[\log_3(x)=3\]?

Answer 17

3^3.. haha

Answer 18

found that 27 after all didn't you?

Answer 19

so the reason I give the 3 on the right side logbase3 is to make my life easier to work on the left side, correct?

Answer 20

:) yes.

Answer 21

you do not "give" anything
\[\log_3(\text{whatever})=3\iff \text{whatever}=3^3\]

Answer 22

oh ok, i understand... thank you so much