Solve log3x +log9 = 0

Question

myininaya · Answer

write the left hand side as one log expression

sphott51 · Answer

Log(27x) = 0 ?

myininaya · Answer

then use the following:
$$\log_a(1)=0 \ \text{ so if you have } \log_a(f(x))=0 \text{ then } f(x)=1 $$

anonymous · Answer

$$
\begin{align*}
\log{3x} + \log{9} &= 0\
\log{(3\cdot9)x} &= 0\
10^{\log{27x}} &= 10^0\
27x &= 1\
x &= \frac{1}{27}
\end{align*}
$$

anonymous · Answer

The above assumes log base 10, replace ten with any other base you use.

sphott51 · Answer

Yeah that's what I got but that's not one of my answer choices @adolm

myininaya · Answer

what are the choices?

myininaya · Answer

decimal format?

myininaya · Answer

maybe they want you to round your answer to like the nearest hundredth or something?

myininaya · Answer

if so 1/27 wouldn't be appropriate
because it is exact form

anonymous · Answer

Maybe. That would be weird in algebra though.

myininaya · Answer

you could divide 1 by 27 though

sphott51 · Answer

Yeah still not it.. @myininaya

anonymous · Answer

What are the options?

sphott51 · Answer

a. 27 b. 0.04 c.3 d. 0.33 
a is wrong btw..

anonymous · Answer

It's b:
$$
\frac{1}{27} \approx 0.0370370 \approx 0.04 \text{(rounded)}
$$

sphott51 · Answer

ohh.. that makes sense....

anonymous · Answer

Not the best answers.