Solve algebraically: log(x)=-(3/2)

Question

anonymous · Answer

Use the log formula! 

$$\huge \log_ba=c \rightarrow b^c=a$$
**Here we can assume that the log has a base 10 since it is not defined for us already. So b = 10.

noseboy908 · Answer

Ok, that gives us $$10^-(3/2)=x$$

noseboy908 · Answer

How would I go about simplifying further?

anonymous · Answer

Is the -(3/2) in the exponent? If so, then it looks good to me! Not sure if your teacher wants you to simplify that further, but if it doesn't specify then I wouldn't.

noseboy908 · Answer

Great!

anonymous · Answer

Ah okay, haha. Well, let's split up the fraction, yea?
$$\huge 10^{-(3/2)}=(10^{-3})^{1/2}= \sqrt{\frac{1}{10^3}}$$

anonymous · Answer

That's if you wanted to simplify it further. But like I said, it kinda seems better and looks nicer to keep it the other way. Depends on what your teacher wants

noseboy908 · Answer

Looks good to me. Could you assist me in finishing up a trig problem?

anonymous · Answer

I have to go right now, as a matter of fact. But if you still need help when I get back, I'll gladly help you! :)

noseboy908 · Answer

Very well. Thank you for your help!

anonymous · Answer

You are very welcome X)