Question

1/3 log x^2 + 1/3 log 27x=log 9

Answer 1

Please show me the steps. I got 3 and I think thats incorrect.

Answer 2

3 seems to be right :)

Answer 3

@lgbasallote. Okay I checked my answer in wolfram and it says the answer should be -2 log^2(3)/log (9)-1. ??

Answer 4

Are these your steps?

Answer 5

No. I got 3 and the above is another answer that was online. I need to know which one is correct and if its the other one I need to know how they got that.

Answer 6

I got 1/3. :|

Answer 7

ok let me try it again...

Answer 8

http://puu.sh/txcq

Answer 9

@zepp log(2) + log(x)?

Answer 10

log(27) + log(x)

Answer 11

http://www.wolframalpha.com/input/?i=%281%2F3%29+log%28x%5E2%29+%2B+%281%2F3%29log+%2827x%29+%3D+log%289%29 @math102

x = 3

Answer 12

@zepp where did the 1/3 go again?

Answer 13

What 1/3? D:

Answer 14

you know 1/3 log x + 1/3 log (27x) those 1/3

Answer 15

im pretty sure you multiply them somewhere?

Answer 16

yeah

Answer 17

uh

Answer 18

http://puu.sh/txh1 that?

Answer 19

\[\Large \log x^{\frac{2}{3}} + \log (3 x^{\frac{1}{3}}) = \log 9\]
\[\Large \log (3 x^{\frac{2}{3}} + \frac{1}{3}) = \log 9\]

\[\Large \log (3x) = \log 9\]

\[3x = 9\]
\[x = 3\]

Answer 20

the 4th to the last line should be

\[\Large \log (3x^{(\frac{2}{3} + \frac{1}{3})})\]

Answer 21

\[ \begin{align}
\frac{1}{3} \log x^2 + \frac{1}{3} \log 27x &= \log 9 \\
\left( \frac{1}{3} \right) \left( \log x^2 + \log 27x \right) &= \log 9 \\
\log x^2 + \log 27x &= 3\log 9 \\
\log \:(x^2 \times 27x) &= 3\log 9 \\
\log 27x^3 &= 3\log 9 \\
3\log 3x &= 3\log 9 \\
\log 3x &= \log 9 \\
3x &= 9 \\
x &= 3
\end{align} \]

Answer 22

how come align& doesnt work for me -_-

Answer 23

begin{align}
\frac{1}{3} \log x^2 + \frac{1}{3} \log 27x &= \log 9 \\
\left( \frac{1}{3} \right) \left( \log x^2 + \log 27x \right) &= \log 9 \\
\log x^2 + \log 27x &= 3\log 9 \\
\log x^2 \times 27x &= 3\log 9 \\
\log 27x^3 &= 3\log 9 \\
3\log 3x &= 3\log 9 \\
\log 3x &= \log 9 \\
3x &= 9 \\
x &= 3
end{align}

This is exactly how it was written inside the brackets, omitting the \ in front of begin and end to avoid magic

Answer 24

noticing & is in every line and a line break "\\" ends each line

Answer 25

uhmm what does the & do? all the & aligns?

Answer 26

Yeah. In this case, I made it all line up on the equals sign

Answer 27

ohh nice trick