Question

logx+ log(x+2)=log9
solve for x

(the logs are all base 2)

Answer 1

log(a * b) = log(a) +log(b)

Answer 2

You'll want to keep the following log rule in mind:
\[\log ab = \log a + \log b\]We can use this rule to make the left side of your equation into one single log that looks like this:
\[\log x(x+2) = \log 9\]

Answer 3

and then what do i do?
divide by logs?

Answer 4

\(\huge \log_2 x(x+2) = \log_2 9\) that is

Answer 5

You can "cancel" out the logs by taking 2 to the power of both sides. Or, you can realize that since we have the same base log on both sides, and they're equal, the values inside the log must be equal so:
\[x(x+2) = 9\]

Answer 6

okay. ya, so i got that part.. but then what do i do? bec to solve for x i got sqrt 10 -1

Answer 7

You can distribute the x through the parenthesis and then subtract 9 from both sides to get a quadratic:
\[x^2 + 2x -9 = 0\]From here you can solve using the quadratic formula.

Answer 8

I just checked it and got your answer as well, you can check it by plugging it in.

Answer 9

so it makes sense to be that answer?i just think its so weird...

Answer 10

Yep, you got the right answer. You can prove this by plugging it in and checking it.

Answer 11

thnx