## anonymous 5 years ago logx^1/64 =-3/2

1. anonymous

Assuming I interpret your notation correctly,$\log{x^{\frac{1}{64}}}=-\frac{3}{2}\rightarrow \frac{1}{64}\log{x}=-\frac{3}{2}$So$\log{x}=64 \times -\frac{3}{2}=-96$Hence,$x=e^{-96}$

2. anonymous

This is log base 10 not log base e or natural log so the answer should be: $x=10^{-96}$

3. anonymous

Doesn't have to be.

4. anonymous

Yeah it does unless you change the base for x. log and ln are not equivalent. put it in a TI-89 or some math program

5. anonymous

Well, it's a matter of definition. Log is technically the notation for natural logarithm in general, with ln reserved for use as the natural logarithm of the magnitude of a complex number. It's semantics. Mathematicians use log.

6. anonymous

in maths log means base 10 not e unless it is mentioned.

7. anonymous

Whatever. I have a degree + postgrad. in the subject. I'm not arguing about it anymore. Mathematicians use log for ln unless the base is made explicit.

8. anonymous

srry then.