# Homework Help: Using logs in calculations

1. Nov 9, 2006

### John O' Meara

I wish to find the value of .8^(2/5) using logs. I can find the value of .8^(-2/5) as follows: =(log(8)X1/10)X-2/5
=(-1 + .9031)X-2/5 = (-.0969)X-2/5 = +.03876;
antilog(.03876) = 1.093;
Now to find .8^(2/5) my approach is the same:
log(.8)X2/5 = (log(8)X10^-1)X2/5
= (bar1 + .9031)X2/5 : what do I do next. (bar1 = -1)

2. Nov 9, 2006

### Integral

Staff Emeritus
It is hard to understand what you have done.

$$\log( .8^ \frac 2 5 )$$

$$= \frac 2 5 \log (.8)$$
$$= \frac 2 5 ( \log (8) - \log (10))$$

Excell tells me the answer should be ~.915

Last edited: Nov 9, 2006
3. Nov 9, 2006

### HallsofIvy

John O'Meara's work looks exactly like what I used to do in highschool. (Of course, we did all calculations on an abacus back then!). Since a table of logarithms only gave logarithms for numbers between 1 and 10, write .8 as 8 x 10-1. Then log(.8)= log(8)- 1! It's hard to imagine anyone today doing it that way- a calculator will give immediately that log(.8)= -0.096910013008056414358783315826521, far more accurate than any table would be. 2/5 times that is
-0.038764005203222565743513326330608. (I got that, by the way, from the calculator supplied with Windows.)

Integral, log(.8) is negative. The value you give can't possibly be right.

4. Nov 10, 2006

### Integral

Staff Emeritus
Clarifcation:
My Excell value is for $.8 ^ \frac 2 5$ not the log.

5. Nov 11, 2006

### HallsofIvy

Ah! Okay.

John O'Meara, after you have (-1+ .9031)X2/5 the obvious "next thing to do" is the multiplication: -2/5+ .36124= -.4+ .361234= -1+ .6+ .361234= -1+ .961234. Now look that up in the "body" of whatever log tables you are using: find the x that gives that logarithm. More simply you can use the calculator that comes with Windows to find the 'inverse' log of that: the inverse log of .961234 is 9.146056 so we have 9.146056x 10-1= 0.9146056. Actually, it is not at all difficult to use the Windows calculator to do .8.4 directly and see that that is, in fact, the correct answer.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook