Question

Can someone please explain to me home to work this logarithmic equation, I have finals Monday!!!! Solve: 2 log3 (x+2)=log3 9+2

Answer 1

typo *how

Answer 2

deja vu, that strange feeling you get when you think you have been there before

Answer 3

I'm sorry lol I just don't get it

Answer 4

\[2\log_3(x+2)=\log_3(9)+2\] and if it says in the problem

\[2\log_3(x+2)=\log_39+2\] it means the same thing
first thing we do is change
\[\log_39\] to 2 because
\[3^2=2\] is that part ok?

Answer 5

O k.....

Answer 6

\[\log_b(x)=y\iff b^y=x\] so
\[\log_3(9)=2\iff 3^2=9\]

Answer 7

okay got u

Answer 8

so now we have
\[2\log_3(x+2)=2+2=4\] divide both sides by 2 to get
\[\log_3(x+2)=2\] so far so good?

Answer 9

Where did the 2+2=4 come from?

Answer 10

original problem had
\[\log_39+2\] on the right, and since
\[\log_39=2\] we get
\[\log_39+2=2+2=4\]

Answer 11

Okay

Answer 12

now divide by 2 to get
\[\log_3(x+2)=2\]

Answer 13

and rewrite in "equivalent exponential form" meaning change
\[\log_b(x)=y\text { to } b^y=x\] so turn this into
\[3^2=x+2\]

Answer 14

then solve for x by subtracting 2 from both sides

Answer 15

Okay thank you much :)

Answer 16

yw